Math Riddle
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Math Riddle
Usually I am able to mentally deduce math riddles immediately upon seeing them. However, even after calculator work, I could not figure out the following (with the *correct* answer):
"Kevin's electricity costs him 22 cents per kilowatt every hour. He's decided to install solar cells on his roof for $40,000, which will save 5% on his power bill.
How many days will it take to pay for itself if Kevin uses 454 kilowatts every hour of every day?"
Before I give the "correct" answer, I want to see how you do on this.
(This was found on "The Brain Game" 2009 Calendar, and as far as I've found, a Google search yields nothing.)
Include work.
"Kevin's electricity costs him 22 cents per kilowatt every hour. He's decided to install solar cells on his roof for $40,000, which will save 5% on his power bill.
How many days will it take to pay for itself if Kevin uses 454 kilowatts every hour of every day?"
Before I give the "correct" answer, I want to see how you do on this.
(This was found on "The Brain Game" 2009 Calendar, and as far as I've found, a Google search yields nothing.)
Include work.
Re: Math Riddle
Spoiler:
I'm guessing I'm wrong, since that seems pretty obvious.
Re: Math Riddle
I did it a little differently.
I mean is there some trick that makes the obvious answer wrong?
Spoiler:
I mean is there some trick that makes the obvious answer wrong?
Re: Math Riddle
Does his power bill decrease after the installation or does he just consume more power to equal the previous bill?
Under the assumption that it doesn't (because then the solar panel would never pay for it self):
Are we all wrong?
Under the assumption that it doesn't (because then the solar panel would never pay for it self):
Spoiler:
Are we all wrong?
Industrial Software Specialist.

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Re: Math Riddle
You are all getting the same answer that I did!
Spoiler:
Re: Math Riddle
chocolate.razorblades wrote:You are all getting the same answer that I did!Spoiler:
It could be that they meant to say that he uses 454 kilowatt hours per day and his rate is $0.22/kWh. $2,000 seems a bit high for a per day for electricity. So that would make the time it take for the panels to pay for themselves 24 times longer, since you're dividing the energy use by 24. Multiplying the answer everyone's getting by 24 yields the correct answer.
I think the question may have simply been poorly phrased or a typo or something.
Re: Math Riddle
Since Kevin is using approximately five thousand times as much electricity as the average person (read: me), I imagine the Feds will figure out what that power is for and bust him before the solar panels can pay for themselves.
Re: Math Riddle
hm... my answer to that is 16.686690695501268188492858096382 days...
Oh me yarm how much electricity does he use?
Oh me yarm how much electricity does he use?
Re: Math Riddle
Buttons wrote:Since Kevin is using approximately five thousand times as much electricity as the average person (read: me), I imagine the Feds will figure out what that power is for and bust him before the solar panels can pay for themselves.
hahahahah xD Oh me yarm there's something wrong with you!!
Re: Math Riddle
Ieatsoap6 wrote:It could be that they meant to say that he uses 454 kilowatt hours per day and his rate is $0.22/kWh. $2,000 seems a bit high for a per day for electricity. So that would make the time it take for the panels to pay for themselves 24 times longer, since you're dividing the energy use by 24. Multiplying the answer everyone's getting by 24 yields the correct answer.
I think the question may have simply been poorly phrased or a typo or something.
*Smacks head* Duh. I guess I really am a mathematician inside, since I saw absolutely no problem with the idea of a $60 000 per month electricity bill.
Re: Math Riddle
Can we assume he deposits the monthly savings into an interestbearing account that compounds daily?
wee free kings
Re: Math Riddle
Nyktos wrote:*Smacks head* Duh. I guess I really am a mathematician inside, since I saw absolutely no problem with the idea of a $60 000 per month electricity bill.
I think he could cover the 60 grand by selling the pot that he growing in his basement.
Industrial Software Specialist.
Re: Math Riddle
I got 8009.611534 days. Would you really only save 5% on electricity with a $40,000 solar panel setup?
Edit: Oh, right. Show your work.
Edit: Oh, right. Show your work.
Spoiler:
Re: Math Riddle
Can we further assume he would have otherwise invested the 40 grand into the same interestbearing account?
If so, at what interest rate would the solar panels switch from "Paying themselves off in a finite amount of time" to "Never paying themselves off"? What if the interest is compounded continuously?
If so, at what interest rate would the solar panels switch from "Paying themselves off in a finite amount of time" to "Never paying themselves off"? What if the interest is compounded continuously?
wee free kings
Re: Math Riddle
And if Kevin's electricity consumption were remotely normal (let's be generous and say $300/month, which is what you might expect using space heaters or air conditioning at all times), then it'll take more than a century for the solar panels to pay for themselves anyway.
 jestingrabbit
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Re: Math Riddle
Its normal to always have something on altering the temp? Really? Because I go more than six months of the year with no such object.
And seriously, $300 a month? When I have to pay that for 3 months I'm pissed off. Or is this for a family or something?
And seriously, $300 a month? When I have to pay that for 3 months I'm pissed off. Or is this for a family or something?
ameretrifle wrote:Magic space feudalism is therefore a viable idea.
Re: Math Riddle
jestingrabbit wrote:Its normal to always have something on altering the temp? Really? Because I go more than six months of the year with no such object.
And seriously, $300 a month? When I have to pay that for 3 months I'm pissed off. Or is this for a family or something?
I dunno, I was trying to shoot for as big a number as possible. Our bill is usually $25 or so, but our neighbors use space heaters and were paying $250 during the coldest months.
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Re: Math Riddle
Qaanol wrote:Can we further assume he would have otherwise invested the 40 grand into the same interestbearing account?
If so, at what interest rate would the solar panels switch from "Paying themselves off in a finite amount of time" to "Never paying themselves off"? What if the interest is compounded continuously?
I'd say that assumption is more or less cancelled out by the assumption that electricity remains at a constant price for the next couple decades.
Re: Math Riddle
Electricity bills usually aren't linear either. My dad has solar panels on his roof and saves more money (% of normal bill) than power he produces (% of power consumed) because the solar panels take off the top kWh, which are the most expensive.
Re: Math Riddle
The answer of 8009 is 100% correct.
Where you're probably going wrong, is with the units.
(question copied here for my convenience :p)
"Kevin's electricity costs him 22 cents per kilowatt every hour. He's decided to install solar cells on his roof for $40,000, which will save 5% on his power bill.
How many days will it take to pay for itself if Kevin uses 454 kilowatts every hour of every day?"
Problems like these can be dramatically simplified when considering the units.
Where you're probably going wrong, is with the units.
(question copied here for my convenience :p)
"Kevin's electricity costs him 22 cents per kilowatt every hour. He's decided to install solar cells on his roof for $40,000, which will save 5% on his power bill.
How many days will it take to pay for itself if Kevin uses 454 kilowatts every hour of every day?"
Spoiler:
Problems like these can be dramatically simplified when considering the units.
 gmalivuk
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Re: Math Riddle
mrmitch wrote:(where'd I get this? he uses 454kW * 24 hour = 1 day, 1 day = 24 hour, giving 454kWh/day)
No, that's wrong. You didn't simplify the question, you just made it wrong.
454kW * 24hr = 10896 kWh, and that's in one day. 10896 kWh/day, in other words. I'm sure you got what the question writer intended, but that's not what the question actually says.
Re: Math Riddle
nevermind.. once I actually read it I felt stupid that I had missed that I forgot to convert hours to days .
Re: Math Riddle
No, that's wrong. You didn't simplify the question, you just made it wrong.
454kW * 24hr = 10896 kWh, and that's in one day. 10896 kWh/day, in other words. I'm sure you got what the question writer intended, but that's not what the question actually says.
Actually, I did realise that this morning when I woke up, having posted that at a very early hour.
To be honest, I have no idea why or I confused myself, probably upon simplifying the explanation. Anywho, I just shouldn't have simplified to letters.
Spoiler:
Re: Math Riddle
mrmitch wrote:Bill is 0.22 dollars / (kW every hour)
Savings is 5% so you are saving 0.05 * .22 dollars / kW every hour = 0.011 dollars / kW every hour
He uses 454 (kW every hour)/ day
The correct calculation would be 454 (kW every hour) * 24 hours/day, making the answer 334 days.
As gmalivuk said, though the author of the question probably meant to say 454 kwh every day, he said every hour. However the answer to the question as written is 334 days.
Re: Math Riddle
I am reporting this to the bureau of poorly stated word problems.
Re: Math Riddle
The correct calculation would be 454 (kW every hour) * 24 hours/day, making the answer 334 days.
As gmalivuk said, though the author of the question probably meant to say 454 kwh every day, he said every hour. However the answer to the question as written is 334 days.
No, treat kW every hour as a unit, and it all makes sense. He probably meant kWh by kW every hour. There is no conversion required  the units are already 454 (kW every hour)/day and the cost is $/kW every hour.
So multiplying cancels out kW every hour giving you $ and days allowing you to solve the problem.
I like to apply dimensional reasoning to questions which just don't make sense/badly worded.
 gmalivuk
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Re: Math Riddle
mrmitch wrote:He probably meant kWh by kW every hour.
Yes, but that would be wrong.
Because if I go 10 meters every second, it's 10 m/s, not 10 m*s.
The problem as stated is worded incorrectly if the answer they want is 8009 days. "Fixing" that mistake by then interpreting something in a way that would be incorrect for any properly worded question isn't really helping anyone.
Re: Math Riddle
Yes it would be wrong, however, the question is still attemptable  by treating "kW every hour" as a unit, as I have done.
Actually, even as kW every hour as kW/h, that's perfectly fine.
Cost = $0.22/(kW/h)
Savings = $0.011../(kW/h)
Usage = 454 kW/hdays
multiplying savings * usage (cost * usage = price, etc)
yields 4.994/d *x days = $40000
solving for x gives 8009.
There is actually nothing wrong with the problem, we've just all assumed things and followed along with them. By sticking with the facts, as you should do with any problem, the question remains valid and you are claim is not.
If you consider reality, it is obvious the author meant kWh instead of or as kW every hour, however, given this mistake, it doesn't matter. As I have shown, the question is still valid.
Actually, even as kW every hour as kW/h, that's perfectly fine.
Cost = $0.22/(kW/h)
Savings = $0.011../(kW/h)
Usage = 454 kW/hdays
multiplying savings * usage (cost * usage = price, etc)
yields 4.994/d *x days = $40000
solving for x gives 8009.
There is actually nothing wrong with the problem, we've just all assumed things and followed along with them. By sticking with the facts, as you should do with any problem, the question remains valid and you are claim is not.
If you consider reality, it is obvious the author meant kWh instead of or as kW every hour, however, given this mistake, it doesn't matter. As I have shown, the question is still valid.
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Re: Math Riddle
mrmitch wrote:Actually, even as kW every hour as kW/h, that's perfectly fine.
Sure, but then you get a completely different answer. Because you have power per time, instead of power * time (which is energy, which is proportional to cost)
"Kevin's electricity costs him 22 cents per kilowatt every hour." In other words, cost is (22 cents / kW) / hour, which we can simplify to 22 cents / (kWh). There is no reason to treat that sentence as actually meaning 22 cents per (1 kilowatt every hour). Especially as electricity is charged by the kWh, not by the kW/h.
So yes, there most definitely *is* still something wrong with the question as stated. It is poorly worded, because the most natural way to read any part of it leads to an answer different from the one they wanted people to get.
Re: Math Riddle
I read it that he was using 454kWh/day after he installed the solar panels, so...
Spoiler:
Re: Math Riddle
."Kevin's electricity costs him 22 cents per kilowatt every hour." In other words, cost is (22 cents / kW) / hour, which we can simplify to 22 cents / (kWh). There is no reason to treat that sentence as actually meaning 22 cents per (1 kilowatt every hour). Especially as electricity is charged by the kWh, not by the kW/h.
No, you still get the same answer, and as I said, where you're going wrong is the units. He gets charged (and hence saves) by his "kW every hour" as stated in the question, so no matter how you want to represent this, it doesn't matter, because he uses some amount of kW every hour, every day. So as I have said, you must multiply these two rates together to get his savings every day, which then allows you to find the amount of days.
Even if, as you say, there is no reason to treat the sentence meaning as such, as you have stated (correctly) electricity is charged by kWh 's, it still works perfectly fine. Since electricity is charged by kWh, you'd say the rate is $/kWhday, and multiplying the two together still works as expected. Then yes, there is a problem with the wording. But it doesn't matter, for any question with the same circumstances, "kW every hour," or a similar such phrase, can always be treated as a unit, as per dimensional reasoning.
I still don't know why you are ignoring this fact.
Re: Math Riddle
Ok guys, your problem is the unit kWh. You've clearly never looked at an electric bill before.
A standard "unit" of power is the kilowatt * hour. This means the amount of energy consumed at a 1 kW rate for 1 hour.
For example:
A 1000 W toaster running for 1 hour = 1 kWh
A 100 W light bulb running for 10 hours = 1 kWh
A 10 W night light running for 100 hours = 1 kWh
They all used the exact same amount of energy, just at different rates.
So when subby says 454 kWh, he means 454 kWh used per day, not 454 kWh * 24 hours per day. The time is already taken into consideration in the unit.
For more information, see the everhelpful Wikipedia page on it.
BTW, 22 cents per kWh seems a little high for the U.S., at least based on this link.
EDIT: Got all semanticy on myself.
A standard "unit" of power is the kilowatt * hour. This means the amount of energy consumed at a 1 kW rate for 1 hour.
For example:
A 1000 W toaster running for 1 hour = 1 kWh
A 100 W light bulb running for 10 hours = 1 kWh
A 10 W night light running for 100 hours = 1 kWh
They all used the exact same amount of energy, just at different rates.
So when subby says 454 kWh, he means 454 kWh used per day, not 454 kWh * 24 hours per day. The time is already taken into consideration in the unit.
For more information, see the everhelpful Wikipedia page on it.
BTW, 22 cents per kWh seems a little high for the U.S., at least based on this link.
EDIT: Got all semanticy on myself.
Re: Math Riddle
famousp: I'm sure that everyone here already knows that kWh is the standard unit of energy (not power) used in an electricity bill. Let's look at the references to power/energy in the actual problem statement though.
This states that electricity costs 22 cents per kWh. It's an unusual way to phrase it, but that's the only reasonable interpretation. Nobody is disputing this part, as far as I know.
I fail to see any reasonable interpretation of this clause other than "Kevin uses 454 kilowatts of power continuously, 24 hours a day, 7 days a week, 365.2422 days a year." I certainly don't see any way to interpret it as "Kevin uses 454 kWh per day" while remaining consistent with the rules of English grammar. If the latter interpretation is intended, then the problem is stated incorrectly.
Kevin's electricity costs him 22 cents per kilowatt every hour.
This states that electricity costs 22 cents per kWh. It's an unusual way to phrase it, but that's the only reasonable interpretation. Nobody is disputing this part, as far as I know.
Kevin uses 454 kilowatts every hour of every day
I fail to see any reasonable interpretation of this clause other than "Kevin uses 454 kilowatts of power continuously, 24 hours a day, 7 days a week, 365.2422 days a year." I certainly don't see any way to interpret it as "Kevin uses 454 kWh per day" while remaining consistent with the rules of English grammar. If the latter interpretation is intended, then the problem is stated incorrectly.
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Re: Math Riddle
Nitrodon wrote:Kevin's electricity costs him 22 cents per kilowatt every hour.
This states that electricity costs 22 cents per kWh. It's an unusual way to phrase it, but that's the only reasonable interpretation. Nobody is disputing this part, as far as I know.
Actually, I think mrmitch is, when claiming that we should take (kilowatt every hour) as its own unit in this case. Which is stupid, because that would be like taking (second every second) as a unit in "His speed was changing by a meter per second every second". So it's true, as you say, that the other interpretation is the only reasonable one.
But then when we come to the second part, as you also say, there's no indication whatsoever that now "kilowatts every hour" means kWh, and the "of every day" part just tells us his usage is constant.
Re: Math Riddle
Which is stupid, because that would be like taking (second every second) as a unit in "His speed was changing by a meter per second every second".
It's not like taking second every second as a unit in "his speed was changing by a meter per second every second." First of all, who would say such a thing, and second of all, they're totally different scenarios. Dimensional reasoning works and validates the question, whether you like it or not.
It would, however, work if it was a similar situation. If, for example, there was some rate against second every second, it would work. This is pointless, because there probably doesn't exist such a rate, unless you invent one.
Re: Math Riddle
You're still arguing that 1 kW every hour of every day is some how just 1kWh a day, which is clearly wrong.
You can use 1 kW for an hour, or one kWh an hour, but 1000 joules a second every hour makes no sense.
You can use 1 kW for an hour, or one kWh an hour, but 1000 joules a second every hour makes no sense.
Re: Math Riddle
ian wrote:You're still arguing that 1 kW every hour of every day is some how just 1kWh a day, which is clearly wrong.
You can use 1 kW for an hour, or one kWh an hour, but 1000 joules a second every hour makes no sense.
It does as a measure of the rate of change of power. Maybe in the OP they're charging him for changing how much power he uses, rather than how much he uses. Interpreting it literally, that's what it says.
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Re: Math Riddle
ian wrote:You're still arguing that 1 kW every hour of every day is some how just 1kWh a day, which is clearly wrong.
You can use 1 kW for an hour, or one kWh an hour, but 1000 joules a second every hour makes no sense.
Actually, I'm not.
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Re: Math Riddle
mrmitch wrote:It's not like taking second every second as a unit in "his speed was changing by a meter per second every second." First of all, who would say such a thing,
Sounds pretty reasonable to me. What's wrong with it?
Re: Math Riddle
That's not what I was referring to, however, I'd like for the mod to stop posting statements without proving them. In maths, as you should all know, proofs require us to step from one truth to another. Do not state things without backing them up.
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