SOLUTION: A Hudson RIVER tugboat goes 10 mph 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?

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Question 344571: A Hudson RIVER tugboat goes 10 mph 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 Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
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R%2At=D
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Let C be the current speed.
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Upstream, against the current,
1.%2810-C%29t%5B1%5D=24
Downstream, with the current,
2.%2810%2BC%29t%5B2%5D=24
Total time,
3.t%5B1%5D%2Bt%5B2%5D=5
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From eq. 1,
t%5B1%5D=24%2F%2810-C%29
From eq. 2,
t%5B2%5D=24%2F%2810%2BC%29
Substitute into eq. 3,
24%2F%2810-C%29%2B24%2F%2810%2BC%29=5
24%2810%2BC%29%2B24%2810-C%29=5%2810%2BC%29%2810-C%29
240%2B24C%2B240-24C=5%28100-C%5E2%29
480=5%28100-C%5E2%29
96=100-C%5E2
C%5E2=4
highlight%28C=2%29mph