A boat can travel 21mph in still water. If it travels 270 miles with the current in the same length of time it travels 108 miles against the current, what is the speed of the current?

Answer: the speed of the current is 9 mph.

Step-by-step explanation:

Let x represent the speed of the current.

A boat can travel 21 mph in still water. If it travels 270 miles with the current. It means that the total speed with which the boat travelled with the current is (21 + x) mph.

Time = distance/speed

Time spent by the boat in travelling 270 miles is

270 / (21 + x)

In the same length of time, it travels 108 miles against the current. It means that the total speed with which the boat travelled against the current is (21 - x) mph.

Time = distance/speed

Time spent by the boat in travelling 108 miles is

108 / (21 - x)

Since the time is the same, then

270 / (21 + x) = 108 / (21 - x)

270 (21 - x) = 108 (21 + x)

5670 - 270x = 2268 - 108x

108x + 270x = 5670 - 2268

378x = 3402

x = 3402/378

x = 9