## Last Call

A forum for good logic/math puzzles.

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Jayraj
Posts: 15
Joined: Sun Oct 21, 2018 11:06 am UTC

### Last Call

As you flip the last switch on the dial, you see the whole radio bench light up and you hear static on the loudspeaker.

Breathing a sigh of relief, you hurry to the microphone and attempt to contact whoever might be listening.

You don't even need to play around with the frequency before someone answers your call, asking for identification.

Keeping your calm, you convey the entire story to the person on the radio, along with the details you deem useful to verify your account.

You are told that the island was abandoned in haste due to increasing volcanic activity and imminent risk of eruption.

Due to worsening weather conditions, an aerial rescue is not possible, so a rendez-vous is set up at the point where you disembarked on the island,

where a military cruiser will come pick you guys up as soon as possible.

As you go outside, you realise how dark the sky really is even though it is still day time, there is a huge pillar of smoke rising south of your position.

You can even see lightning in and around it.

You all get on the lorry and head to your rendez-vous point, with everybody in high spirits.

You are almost there when you hear a great boom and feel tremors shaking up your lorry. A few seconds later, you are assaulted with a hail

of burning rocks, littering the road and lighting up the area around you.

As you manage to reach the camp you get out quickly and survey the scene around you.

There is lava flowing down the slopes of the hill towards you and the air is filled with volcanic ash, making breathing difficult.

It would be impossible to wait for the rescue ship here and as you look to the sea for solace you notice a smaller island in the distance.

It looks distant, but it is your only option and you know you can reach it in the lifeboats.

From your initial journey to the island you know that each lifeboat can transport up to 8 passengers and 2 oarsmen.

As you reach the dock you find that only one of the three boats survived the onslaught of projected rocks, crushing your hopes of having all 28 of you leave together.

You estimate the smaller island is only 5 minutes away if you use the lifeboat by yourself.

Most of the passengers either do not know how or are in no condition to swim.

Only the other 5 previous oarsmen still have enough strength left to man the boat.

They were never a match for you though, the fastest one, Kevin, has half your own speed, three of them have a sixth of your speed and the last one, Geerish, a fifth of your speed.

Both rowers need to synchronise their movements in order to keep the boat in track, so if Kevin went with Geerish, they'd both have to move at a fifth of your speed.

The problem is now that you only have one boat to work with, and if you transport passengers, you require 2 oarsmen to move the boat.

However you can ferry people to the island with two rowers and then come back with only one rower in the lifeboat.

What is the minimum amount of time required to ferry everyone to the island and thus escape the lava?

Note:

Desperation fuels their determination and no matter how many trips they have to make, they never slow down.

Yat
Posts: 131
Joined: Tue Feb 03, 2009 2:05 pm UTC

### Re: Last Call

So, if I get the explanations correctly, there are 6 oarsmen including me, their crossing times are 5, 10, 25, 30, 30 and 30 minutes. That is, assuming I can still able to row the boat, which doesn't seem to be very clear. Again, it seems implied that the boat can be handled by a single oarsman when there are no passengers.

Spoiler:
Each trip forward moves 10 people, each trip back moves back one person. three forward trips and two trips back allow to move everybody. The trick is to make one forward trip with slow oarsmen to allow the other two (and the trips back) to be made much more quickly.
The first trip with 5,10 takes 10 minutes. Then 5 goes back in 5 minutes.
The next trip takes 30 minutes, because pairing 5 with 25 to gain 25 minutes would considerably slow the last trip down, so 5 stays there. 10 goes back in 10 minutes.
Final trip, 5 and 10 row again, for a 10 minutes trip.
Total: 65 minutes.