Question

A boat can travel 8 mph in still water. If it can travel 15 miles downstream in the same time that it can travel 9 miles up the stream, what is the rate of the stream?

Answer 1

`9 1/7" miles per hour"`

Explanation:

Let the time of travel in each direction be `t`

Let the velocity of the water be `v`

Let distance be `s`

Given that the boat velocity is 8 mph

Downstream `-> s= (8+v)t=15`.....................Equation(1)

Upstream `-> s=(8-v)t=9`...........................Equation(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Write Eqn(1) as: `8t+vt=15 .........................................(1_a)`
Write Eqn(2) as: `8t-vt=9.........................................(2_a)`

`Eqn(1_a)+Eqn(2_a)` gives:

`16t=14 => t=14/16 -=7/8`.............................(3)

Using `Eqn(3)` substitute for `t` in `Eqn(1_a)`

(This should work no matter which equation you choose)

`color(brown)(8t+vt=15)color(blue)(" "->" "8(7/8)+v(7/8)=15`

`v=8/7(15-7) = 64/7" "("miles")/("hour")`