Ben's boat will take 1½ hours longer to go 12 miles up a river than to return. what is the rate of his boat if the rate of the current is 2 miles an hour?

Answer

= 4.8 miles per hours.

Explanation

Let the time taken to run down the river to be t hours.

The time the bout takes to run up the river will be (t+1.5) hours.

Let the rate of the boat to be x miles per hour.

So the speed of the boat up the river will be (x-2) miles per hour due to the drag the the current.

The speed of the boat down the river will be (x+2).

Distance = 12 miles

With this information we can form two equations and solve them simultaneously.

distance = speed × time

12 = (t+3/2)(x-2)

12 = tx-2t+1.5x-3

tx - 2t + 1.5x =15(i)

12 = t(x+2)

t = 12/(x+2)(ii)

Substitute t in equation (i) with 12/(x+2)

tx - 2t + 1.5x =15

12x/(x+2) - 2x/(x+2) +1.5x = 15

12x - 2x +1.5x(x+2) = 15(x+2)

10x + 1.5x²+3x=15x+30

1.5x²-2x-30 = 0

3x² - 2x - 60 = 0

Using quadratic formula;

x = (--2 (+ or -)√(2²+4×3×60))÷(2×3)

x = 4.8 or

x= -4.15.

Since speed cannot be negative, x = 4.8.

Rate of the boat = 4.8 miles per hours.