Question

A motorboat covers a certain distance downstream in a river in 5hours. It covers the same distance upstream in 5 and a half hours. The speed of the water us 1.5km/hr. Find the speed if the boat in still water.

Answer 1

Let the speed of boat in still water = x km/h
speed of water = 1.5 km/h

Speed of boat downstream = (x+1.5) km/h
time taken in downstream journey = 5 hours
distance travelled = 5(x+1.5) km

Speed of boat upstream = (x-1.5) km/h
time taken in downstream journey = 5.5 hours
distance travelled = 5.5(x-1.5) km

Since same distance is covered in both the cases

5(x+1.5) = 5.5(x-1.5)
⇒ 5x + 5×1.5 = 5.5x - 5.5×1.5
⇒ 5x + 7.5 = 5.5x - 8.25
⇒ 5x - 5.5x = -8.25 - 7.5
⇒ -0.5x = -15.75
⇒ x = (-15.75)/(-0.5)
⇒ x = 31.5 km/h