Boat problem and monty hall problem

**carvegio** · 16th August 2006

This is a nice puzzle, but it is quite hard ...

Two ferry boats start at the same instant on opposite sides of the river. One is faster than the other. They cross at a point 720 yards from the left shore on their way to their respective destinations, where each one spends 10 minutes to change passengers before the return trip. They meet again at a point 400 yards from the right shore.
How wide is the river?

and for those that have not heard it before...

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

great puzzle also, try not to cheat

**tawny** · 16th August 2006

1120 yds?

**/dev/null** · 16th August 2006

Yes it is at your advantage to change doors... We did a massive mathematical analysis of the probabilities of such a problem at university, lol!

- If anyone is THAT interested, I'll try & post the file!

**carvegio** · 16th August 2006

Originally Posted by tawny

1120 yds?

not quite

it's a bit higher, if u want a soln could post one in a bit .. dunno if anyone else is trying it, probably not though I guess

the door one is right. The best way of looking at it is if you pick the wrong door, he shows you the other wrong door and if you switch you win. If you pick the right door, he shows you one of the two wrong doors and if you switch you loose. So, if you pick a wrong door you will win if you switch. The probability of picking a wrong door is 2/3, so it's also the probability of winning. Where as if you pick one door and stick the probability of winning is 1/3... so it's double if u switch

**Lee Macro** · 17th August 2006

These are pretty good. Remember the Monty Hall one from a while ago. This one was doing the rounds aorund about the same time

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

**tawny** · 17th August 2006

Originally Posted by Lee Macro

These are pretty good. Remember the Monty Hall one from a while ago. This one was doing the rounds aorund about the same time

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

No way, the wheels would spin but the plane would remain on the ground. Wind must pass over the top and bottom of the wing, travelling faster over the top creating higher airpressure lifting the plane into the sky. The plane could potentially take off if it was a very windy day!

**carvegio** · 17th August 2006

I agree with the above

**Lee Macro** · 17th August 2006

Originally Posted by Lee Macro

These are pretty good. Remember the Monty Hall one from a while ago. This one was doing the rounds aorund about the same time

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

The plane does take off

**Mule** · 17th August 2006

Don't start that bloody plane one again, there's already a huge thread on it.

**TwoPlAnKs** · 19th August 2006

Originally Posted by tawny

No way, the wheels would spin but the plane would remain on the ground. Wind must pass over the top and bottom of the wing, travelling faster over the top creating higher airpressure lifting the plane into the sky. The plane could potentially take off if it was a very windy day!

i really dont want to get into this again but what exactly would make the wheels spin? aeroplanes dont use wheels for driving because there is no ground in the sky

**TwoPlAnKs** · 19th August 2006

Originally Posted by tawny

1120 yds?

they meet once and between them they have travelled the width of the river, and the boat that had gone from the left shore had travelled 720 yards. they meet again, and between them they have travelled 3 times the width of the river. it is therefore the case that the boat which had travelled 720 yards at the first meeting has now travelled three times that, which is 2160 yards. this is the width of the river plus the 400 yards that the boat originally from the left had travelled from the right shore to get back to the left, so the final answer is 1760 yards (or a mile as that is conventionally known)

**Gazzr** · 21st August 2006

Originally Posted by Lee Macro

These are pretty good. Remember the Monty Hall one from a while ago. This one was doing the rounds aorund about the same time

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

The plane would take off. Jet engines / propellor's push the air around the craft. The wheels may spin, or not spin. But the plane would still move forwards over the conveyor /runway, and lift off.
(I think anyway)

**Speshal** · 22nd August 2006

Unless the plane is actually moving it won't take off. Could it take off in a wind tunnel then?

**Gazzr** · 23rd August 2006

The plane would be moving forwards. And yes it could take off in a wind tunnel. Ever seen birds "float" in the air using the wind passing them to provide the lift.

I think you need to remember the wheels are not the propultion forwards. A car in this situation would remain still - as the faster the wheels went, the faster the "belt" went, and the car would not move forwards. Because it uses the wheels to push forwards.
A plane uses thrust. The whole runway could be a conveyor belt but the plane would move over the top of it at normal forwards speed. The belt could move as fast as it wanted in the opposite direction, all it would do is make the wheels spin much faster, but the body of the plane would be un affected.
Still accelerating towards the end of the runway / belt, and gathering speed as it went.
Thats my view of it anyway.

**Speshal** · 23rd August 2006

I can see where you're going with that because with a car the source of motion would be the wheels but the plane would use it's jets (or propellar etc.) therefore the plane isn't restricted by the opposing movement of the belt.

Maybe it would fly then.

/me buys an airplane, conveyor belt and thinking cap.