Janet's boat will go 10 miles per hour in still water. If he can go 120 miles downstream in the same amount of time as it takes to go 40 miles upstream, then what is the speed of the current? Include units in your answer

Answer: the speed of the current is 10 mph.

Step-by-step explanation:

Let x represent the speed of the current.

Janet's boat will go 10 miles per hour in still water. This means that the total speed at which she went downstream is (10 + x) mph.

Time = distance/speed

If he can go 120 miles downstream, then the time taken to go downstream is

120 / (10 + x)

The total speed at which she went upstream is (10 - x) mph. If at the same time, she goes 40 miles upstream, then the time taken to go downstream is

40 / (10 - x)

Since the time is the same, it means that

120 / (10 + x) = 40 / (10 - x)

Cross multiplying, it becomes

120 (10 - x) = 40 (10 + x)

1200 - 120x = 400 + 40x

120x + 40x = 400 + 1200

160x = 1600

x = 1600/160

x = 10 mph