Question

Hagrid rowed his boat upstream a distance of 9 miles and then rowed back to the starting point. The total time of the trip was 10 hours. If the rate of the current was 4 mph, find the rate of the boat in still water. Enter a number only as your answer.

Answer 1

Let take boat speed = x

Current speed = 4

Upstream = x - 4

Downstream = x + 4

Distance = 9

Time upstream + Time downstream = 10

Time = Distance/Speed

9/(x + 4) + 9/(x - 4) = 10

Solving this equation 9(x-4)+9(x+4) = 10(x^2 -16)

9x - 36 + 9x + 36 = 10x^2 - 160

18x = 10x^2 -160

10x^2 -18x - 160 = 0

Now solving the above quadratic equation, we get

x = 5 or x = -16/5

We ignore the negative value.

The answer is 5.

The speed of the boat in still water is 5mph.

Thank you.