Question

A boat downstream from A to B takes 7 hours, upstream from B to 9 hours. How much time does a log take from A to B? (Driftwood along the water velocity)

Answer 1

A log takes `63` hours from `A` to `B`.

Explanation:

Let the distance between `A` and `B` be `x`; the speed of boat be `b` and that of still water be `w`.

Hence speed of boat upstream is `b-w` and speed downstream is `b+w`. Therefore time taken for upstream is `x/(b-w)` and downstream would be `x/(b+w)` and

`x/(b-w)=9` or `b-w=x/9` and similarly

`x/(b+w)=7` or `b+w=x/7`

Hence `b+w-(b-w)=x/7-x/9` or

`2w=(2x)/63` i.e. `w=x/63`

As speed of water is `x/63` and distance is `x`,

it takes `x/(x/63)=x xx 63/x=63` hours.