Question

A motor boat travels 125 kilometers in 5 hours going upstream. It travels 175 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

Let the rate of the boat in still water be x km/h and the rate of the current be y km/h.

When the boat is traveling upstream, it is going against the current so the effective speed is (x - y) km/h. The distance traveled upstream is 125 km and the time taken is 5 hours, so:

125 = 5(x - y)
25 = x - y (equation 1)

When the boat is traveling downstream, it is going with the current so the effective speed is (x + y) km/h. The distance traveled downstream is 175 km and the time taken is 5 hours, so:

175 = 5(x + y)
35 = x + y (equation 2)

Adding equation 1 and equation 2:

25 + 35 = x - y + x + y
60 = 2x
x = 30

Substitute x = 30 back into equation 1:

25 = 30 - y
y = 30 - 25
y = 5

Therefore, the rate of the boat in still water is 30 km/h and the rate of the current is 5 km/h.