A motor boat heads upstream against a constant current of 6

A motor boat heads upstream against a constant current of 6 miles per hour. The trip upstream takes 10 hours and the return trip takes 5 hours. What would the speed of the motor boat be without the current (assume the motor boat maintains a constant speed relative to the water)?

Solution

The problem is related to Distance, Speed and Time.

The relation between these three is Distance=Speed * Time

Let the Speed of motor boat is X miles/hr

Speed of current flow is Y miles/hr

During the Upstream the relative speed of boat is (X-Y) miles/hr = 6 miles/hr

During the Downstream the relative speed of boat is (X+Y) miles/hr

Time taken to trip Upstream = 10 hrs

Time taken to trip Downstream = 5 hrs

Here,Distance for Upstream = Distance for Downstream

(Speed * Time ) for Upstream =   (Speed * Time ) for Downstream

(X-Y)*10 = (X+Y) * 5

6 * 10 = (X+Y) * 5

6 *2 = X+Y

X+Y = 12

The relative speed for Downstream (X+Y) = 12miles/hr

By solving X-Y = 6 and X+Y = 12 we can get X

By adding 2X=18

X=9 miles/hr

Speed of motor boat is X miles/hr

Therefore, Speed of motor boat is 9 miles/hr