SOLUTION: A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes to go upstream the same 8 miles. Find the speed of the current.

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Question 615108: A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes to go upstream the same 8 miles. Find the speed of the current.
Answer by ankor@dixie-net.com(22740) (Show Source):
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A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes to go upstream the same 8 miles. Find the speed of the current.
:
Let s = speed of the boat in still water
Let c = speed of the current
then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
:
since we will wanting mph, change 20 min to 1/3 hr, and 30 min to 1/2 hr
:
Write a distance equation for each way; (dist = time * speed)
(s + c) = 8
(s - c) = 8
multiply the 1st equation by 3, the 2nd equation by 2:
s + c = 24
s - c = 16
---------- adding eliminates c, find s
2s = 40
s = 20 mph boat speed in still water
then
20 + c = 24
c = 24 - 20
c = 4 mph is the speed of the current
:
:
You can confirm this with the distance equation each way