The boat is going 10 miles per hour in still water it takes 2 hours to go downstream and 3 hours to go upstream. What’s the speed of the current and distance of the trip?

Step-by-step explanation:

Let c represent the speed of the current. The travel time is inversely proportional to the travel speed. In one direction the current speed is added to the boat speed; in the other direction, it is subtracted. You can write the relation ...

  (10 +c)/(10 -c) = 3/2

  2(10 +c) = 3(10 -c) . . . . . . "cross multiply"

  20 +2c = 30 -3c . . . . . . . eliminate parentheses

  5c = 10 . . . . . . . . . . . . . . . add 3c -20

  c = 2 . . . . . . . . . . . . . . . . . divide by 5

The speed of the current is 2 miles per hour.

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The speed downstream is then (10 +2) = 12 miles per hour. The travel time in that direction is 2 hours, so the distance covered is ...

  (12 mi/h)(2 h) = 24 mi

The one-way distance of the trip is 24 miles.