Question

In still water, a boat averages 18 miles per hour (mph). It takes the same amount of time to travel 33 miles downstream (with the current) as it takes to travel 21 miles upstream (against the current). What is the rate of the water's current

Answer 1

The rate of the water current is 4mph

Explanation:

Let c= the rate of the current in mph

18+c= the rate of the boat going downstream in mph

18-c= the rate of the boat going upstream in mph

t = time in hrs for both upstream and downstream trips

Going downstream:

33=(18+c)*t (1)

Going upstream

21=(18-c)*t (2)

From (1)

33=(18+c)*t

t=33/1(8+c)

Substitute t=33/(18+c) into (2)

21=(18-c)*t

21=(18-c)*33/(18+c)

Cross product

21(18+c)=33(18-c)

378+21c=594-33c

21c+33c=594-378

54c=216

Divide both sides by 54

54c/54=216/54

c=4

Therefore,

The rate of the water current is 4mph