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A motorboat can maintain a constant speed of 26 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 33 minutes; the return trip takes 19 minutes. What is the speed of the current?

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Answer:

  7 mph

Step-by-step explanation:

A boat whose speed in still water is 26 mph makes a trip upstream in 33 minutes and returns in 19 minutes. You want to know the speed of the current.

Setup

The travel time is inversely proportional to the speed, so we can write the proportion (using c for the current speed in mph) ...

  time upstream / time downstream = speed downstream / speed upstream

  33/19 = (26 +c)/(26 -c)

Solution

Multiplying by 19(26 -c) gives ...

  33(26 -c) = 19(26 +c)

  (33 -19)(26) = (33 +19)c . . . . add 33c -19(26)

  14(26)/(52) = c = 7

The speed of the current is 7 miles per hour.

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