SOLUTION: A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2 mph, find the speed of the boat in still water.

Algebra ->  Human-and-algebraic-language -> SOLUTION: A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2 mph, find the speed of the boat in still water.       Log On


   

Question 40857: A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2 mph, find the speed of the boat in still water.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
let speed of boat in still water be x mph

speed upstream = x-2
speed downstream = x+2

speed = distance/time

So, x-2 = 5/t
and x+2 = 7/t

The time in both journeys is the same, so i have them both as "t". We get:

t = 5/(x-2) = 7/(x+2)
+5%2F%28x-2%29+=+7%2F%28x%2B2%29+
+5%28x%2B2%29+=+7%28x-2%29+
+5x%2B10+=+7x-14+
+10+=+2x-14+
+24+=+2x+
--> x = 24/2
so x = 12 mph

Check:
upstream: speed is 10mph. 5 miles takes 2 hours
downstream: speed is 14mph. 7 miles takes 2 hours too.

jon