Prove: Swimmer's Time in Flowing River = Time in Still Water

[riddhish]

A swimmer crosses a flowing river of width d to and fro in time t1. The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2d in still water, then prove that t1 square = t2t3.

 

[HallsofIvy]

Yes, that's a really great problem! What really great attempts to solve it have you made?

I would let u be the speed of the swimmer in still water, v be the speed of the river. Then write formulas for t1, t2, t3 in terms of d, u, and v. Since there is no u or v given in the problem, you will want to manipulate the equations to eliminate those.

 

[Phrak]

A swimmer crosses a flowing river of width d to and fro in time t1. The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2d in still water, then prove that t1 square = t2t3.

Odd that it take the same time to swim upstream and down...

 

[HallsofIvy]

Good point but I suspect what was meant was that the total time to swim a distance equal to the width of the river upstream and then the same distance back downstream was t2.