It takes a boat 3 hours to travel down a river from point A

It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How many hours would it take the same boat to go from A to B if there was not a river current? Answer:

Solution

Let the speed of the boat be x mph and that of the river current be y mph. When the boat travels from A to B, it takes 3 hours and when it travels from B to A, it takes 5 hours. It means that the journey from A to B is downstream and the boat travels at (x+y) mph during this journey. Also, the journey from B to A is upstream and the boat travels at (x-y) mph during this journey. Since the distance from A to B is same as that from B to A and since distance = speed*time, we have 3(x+y)= 5(x-y) or, 3x+3y = 5x -5y or, 5x-3x = 3y +5y or, 2x = 8y so that x = 4y. Thus, the speed of the boat is 4 times that of the river current.

Now, if the boat travelling at a speed of x+y = 5y, travels a distance in 3 hours, then the boat , travelling at a speed of 4y ( i.e. if there is no current), will cover the same distance in (3/5)*4 = 15/4 hours or, 3.75 hours or, 3 hours, 45 minutes. Thus, the boat will take 3.75 hours or, 3 hours, 45 minutes to travel from A to B if there was no river current.