SOLUTION: With Current, a motorboat travels 60 mi in 3 h. Against the current, it takes 2h longer to travel 60 mi. Find the rate of the current.

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Question 132751: With Current, a motorboat travels 60 mi in 3 h. Against the current, it takes 2h longer to travel 60 mi. 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 boat in still water: r%5Bb%5D
Rate of the current: r%5Bc%5D
Then:
Rate of the boat with the current: r%5Bb%5D%2Br%5Bc%5D
Rate of the boat against the current: r%5Bb%5D-r%5Bc%5D

But we know that r=d%2Ft, so the rate of the boat with the current is 60%2F3=20, and the rate of the boat against the current is 60%2F%283%2B2%29=60%2F5=12, so:

r%5Bb%5D%2Br%5Bc%5D=20
r%5Bb%5D-r%5Bc%5D=12

Add the two equations term by term to eliminate r%5Bc%5D
2r%5Bb%5D=32
r%5Bb%5D=16

Since r%5Bb%5D%2Br%5Bc%5D=20, 16%2Br%5Bc%5D=20, and finally r%5Bc%5D=4

Check:
16 + 4 = 20 mph times 3 hours = 60 miles
16 - 4 = 12 mph times (3 + 2) hours = 60 miles
Answer checks.