A boat travels downstream 120 miles at a speed of 15 mph. On the return trip upstream, the boat travels the same distance but at a speed of 10 mph. What is the speed of the current?
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Let the speed of the current be represented by x mph.
When traveling downstream:
Speed = Boat's speed + Current's speed = 15 mph + x mph = 15 + x mph
Time = Distance/Speed = 120 miles / (15 + x) mph
When traveling upstream:
Speed = Boat's speed - Current's speed = 10 mph
Time = Distance/Speed = 120 miles / 10 mph = 12 hours
Since travel time is equal when traveling upstream and downstream:
120 miles / (15 + x) mph = 12 hours
120 = 12(15 + x) [Simplify]
120 = 180 + 12x [Distribute the 12]
12x = -60 [Subtract 180 from both sides]
x = -5 [Divide by 12]
The speed of the current is 5 mph.
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