Let the speed of Tran's boat be represented by b, and the speed of the current be represented by c.
When Tran is traveling upstream, he is working against the current, so his effective speed is b - c. The distance that he travels upstream is 120 miles, and he completes the trip in 8 hours, so we can write the equation:
120 = (b - c) * 8
When Tran is traveling downstream, he is aided by the current, so his effective speed is b + c. The distance that he travels downstream is also 120 miles, and he completes the trip in 7.5 hours, so we can write the equation:
120 = (b + c) * 7.5
Simplifying both equations, we have:
8b - 8c = 120
7.5b + 7.5c = 120
Dividing the first equation by 8, we get:
b - c = 15
Rearranging this equation, we have:
b = 15 + c
Substituting this value of b into the second equation, we have:
7.5(15 + c) + 7.5c = 120
Distributing and simplifying, we have:
112.5 + 7.5c + 7.5c = 120
Combining like terms, we have:
15c = 120 - 112.5
15c = 7.5
Dividing both sides by 15, we get:
c = 7.5/15
c = 0.5
Substituting this value of c back into the equation b = 15 + c, we have:
b = 15 + 0.5
b = 15.5
Therefore, the speed of Tran's boat is 15.5 mph, and the speed of the current is 0.5 mph.
In his motorboat, Tran travels upstream at top speed to his favorite fishing spot, a distance of 120 miles, in 8 hours. Returning, he finds that the trip downstream, still at top speed, takes only 7.5 hours. Find the speed of Tran's boat and the speed of the current.
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