SOLUTION: Michael rows 8 mph in still water. If he rows 24 miles downstream in the same amount of time he rows 8 miles upstream, find the rate of the current.

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Question 133076: Michael rows 8 mph in still water. If he rows 24 miles downstream in the same amount of time he rows 8 miles upstream, find the rate of the current.



Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
rate of the current: r
downstream rate of the boat: 8 + r
upstream rate of the boat: 8 - r

distance = rate times time, or d=rt, so t=d%2Fr.

Downstream trip: t=24%2F%288%2Br%29
Upstream trip: t=8%2F%288-r%29

Since the times for each trip are equal:

8%2F%288-r%29=24%2F%288%2Br%29

Cross multiply:
8%288%2Br%29=24%288-r%29

Distribute:
64%2B8r=192-24r

Collect like terms:
8r%2B24r=192-64

32r=128

r=4

So the rate of the current is 4.

Check:
8mph + 4mph = 12mph, 24m/12mph = 2 hr
8mph - 4mph = 4mph, 8m/4mph = 2 hr
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