Question

A motor boat covers a certain distance downstream in a river in 5 hours. It covers the same distance upstream in 5 and a half hours. The speed of water is
1.5 km per hour. The speed of boat in still water is?

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

Hence speed of boat in still water is 31.5 km/h.

Answer 2

Answer

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

Hence speed of boat in still water is 31.5 km/h.