A person travels 8 miles down a stream. In the same time they can travel 6 miles upstream. If the current of the river is 2 mph what is the rate of the still boat?

Answer: the speed of the still boat is 14 mph

Step-by-step explanation:

Let x represent the speed of the still boat.

A person travels 8 miles down a stream. Assuming he travels with the current and if the current of the river is 2 mph, it means that the total speed is (x + 2) mph

Time = distance/time

Time spent in travelling with the current is

8 / (x + 2)

In the same time they can travel 6 miles upstream. Assuming he travels against the current, it means that the total speed is (x - 2) mph

Time = distance/time

Time spent in travelling against the current is

6 / (x - 2). since the time is the same, then

8 / (x + 2) = 6 / (x - 2)

Cross multiplying, it becomes

8 (x - 2) = 6 (x + 2)

8x - 16 = 6x + 12

8x - 6x = 12 + 16

2x = 28

x = 28/2

x = 14