Question

The current of a river is 4 miles per hour. A boat travels to a point 30 miles upstream and back in 4 hours. What is the speed of the boat in still water?

Answer 1

let the speed of the board in still water is V

upstream speed = boat speed - current speed = V - 4

downstream speed = boat speed - current speed = V + 4

time taken = distnace/ speed

total time taken = upstream travel time + downstream travel time

4 hours = 30/(V-4) + 30 (V+4)

2/15 = (2V)/(V^2-16)

V^2- 15V - 16 = 0

V^2 - 16V + V - 16 = 0

V(V-16) + 1(V-16) = 0

V = 16 and -1

(V = -1 is not acceptable since board speed should be greater than current speed to travel upstream)

so answer is 16 miles per hours.