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?

1 Answer
Oct 22, 2015

Answer:

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