SOLUTION: A boat goes 10 miles per hour in still water. It travels 24 miles upstream and 24 miles back in a total of 5 hours. What is the speed of the current?

Question 199034: A boat goes 10 miles per hour in still water. It travels 24 miles upstream and 24 miles back in a total of 5 hours. What is the speed of the current?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A boat goes 10 miles per hour in still water. It travels 24 miles upstream and 24 miles back in a total of 5 hours. What is the speed of the current?
.
Apply the distance formula:
d = rt
where
d is distance
r is rate or speed
t is time
.
Solving for t:
t = d/r
.
Let x = speed of current
then rate or speed:
downstream = 10+x
upstream = 10-x
.
24/(10+x) + 24/(10-x) = 5
24(10-x) + 24(10+x) = 5(10+x)(10-x)
240-24x + 240+24x = 5(100-10x+10x-x^2)
480 = 500-5x^2
480+5x^2 = 500
5x^2 = 20
x^2 = 4
x = 2 mph (current)

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