Question

A boat can go 12 mph in calm water. If the boat goes down a river 45 miles and back up the river 45 miles it takes him 8 hours. What is the current of the river?

Answer 1

Let's call the speed of the current `c`

Explanation:

Downstream he will have a speed of `12+c`
and upstream his speed will be `12-c`

Now the downstream journey will take `45/(12+c)` hours

And the upstream journey will take `45/(12-c)` hours

So we get to the equation:

`45/(12+c)+45/(12-c)=8->` make equal denominators

`(45(12-c))/((12+c)(12-c))+(45(12+c))/((12+c)(12-c))=8->`

`(45(12-c+12+c))/(144-c^2)=8->1080/(144-c^2)=8->`

`8*(144-c^2)=1080->1152-8c^2=1080->`

`8c^2=72-> c^2=9->c=3` mph

Check your answer!
Downstream: `45/(12+3)=3` hrs

Upstream: `45/(12-3)=5` hrs