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.

1 answer

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.