SOLUTION: A boat traveled 168 miles downstream and back. The trip downstream took 7 hours. The trip back took 42 hours. Find the speed of the boat in still water and the speed of the curr

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Question 202390: A boat traveled 168 miles downstream and back. The trip downstream took 7 hours. The trip back took 42 hours. Find the speed of the boat in still water and the speed of the current.
Answer by solver91311(24713) About Me  (Show Source):
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Use distance equals rate times time,

Let represent the speed of the boat in still water, and let represent the speed of the current. On the downstream trip, the boat is going with the current, so the total speed is . On the upstream trip, the total speed is

So, the downstream trip can be described by:



which simplifies to:

(Eq. 1)

And the upstream trip can be described by:



which simplifies to:

(Eq. 2)

Add Equation 1 to Equation 2:



Hence the speed of the boat in still water is 14, and:



So the speed of the current is 10.

John