Question

Pratik travels by boat 36 km downstream and back in 8 hours. If the speed of the boat in still water is 12

km/h, find the speed of the water current.​

Answer 1

Answer:

Let speed of water current is x km/h

speed of boat in still water = 12 km/h

Distance = 36 km

Downstream speed = (12 + x) km/h

Upstream speed = (12 - x) km/h

A/C to question,

Total time taken by Pratik = 8 hrs

time taken to travel 36 km downstream + time taken to travel 36 km Upstream = 8hrs

⇒36/(12 + x) + 36/(12 - x) = 8

⇒ 36 [ 1/(12 + x ) + 1/(12 - x) ] = 8

⇒ 9[ {(12 - x) + (12 + x)}/(12² - x²) ] = 2

⇒9 × 24 = 2(144 - x²)

⇒ 9 × 12 = 144 - x²

⇒ 108 - 144 = - x²

⇒ x² = 36

⇒ x = ±6 , but speed ≠ negative

so, x = 6 km/h

Hence, speed of water current is 6 km/h