Who Is Faster?
A man rows a particular distance on a river, with the current, and then rows the same distance against the current. A second man rows the same total distance, as the first man, on a lake where there is obviously no current.
Given that the two men are of equal rowing strength, which takes longer to complete the row?
Given that the two men are of equal rowing strength, which takes longer to complete the row?
posted by Zaux at
10:45 AM
13 Comments:
Man on river takes longest. He could never finish.
I didn't think before posting that. I got carried away with knowing that if the current was fast enough, the first rower wouldn't be able to get back to the starting point.
Let t1 be the time the river rower spends going downstream and t2 for upstream. Let t0 = time taken for the lake rower to do the whole thing.
Then d = (u+v)t1 =(u-v)t2 = ut0/2
Rest is fiddling about to get:
t0/(t1+t2) = 1 - (v/u)²
For the river rower to be able to do the task, 0 < v < u so 0 < v/u < 1. => 0 < 1 - (v/u)² < 1
so t0/(t1+t2) < 1 or t1+t2 > t0. Hence the river rower takes longer than the lake rower.
I've taken a few liberties with signs and have used v > 0 as there is a current.
You guys are so right... next problem --> where to find problems which would be challenging ... heh heh.
The guy on the river. Logically, it would take longer for him to go against the stream, but non his way back with the stream, it carries him probably more than twice as fast without him even having to row. Logistics wins this one boys.
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Hi Nick. Let me try that again. You correctly start by saying that the guy on the river would take longer, but then give an argument that says the opposite. Any doubt I had about your argument was removed by your ironic apology.
If the rower was only a tiny bit faster than the stream, he'd take an enormous amount of time to make the upstream distance d. If he was slower than the stream he'd actually go backwards, and he'd never finish. I find it better to calculate and/or consider limiting cases to check that I've not goofed.
the first person while rowing downstream has advantage and can row faster
then while rowing upstream there is disadvantage and hence will take more time
where as for the second person its all equal if practically we think both will take exact same time
Hi ALAM. Wrong. The disadvantage outweighs the advantage.
the man in the river was faster as he was flowing with the current at the same speed as the current which doubles the speed and cancels out the second row upstream as opposed to the man in the lake were his strenght was the only thing moving him duh!
Anonymous. Imagine someone in a boat rowing at 3 mph in a river that is flowing at 3 mph. He will never get to a destination that is upstream; he'll remain stationary with respect to the river bank.
So duh to you with brass knobs on.
Hi Anonymous. I'm glad you got it. But my last post was bad; I should have phrased it to made it clear that he'd never achieve the first leg of the journey when the river is as fast or faster than the rower.
... another way. Pretend that the river is not moving.
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