Question

Pratik takes 8 hours to travel 36km down stream and to return to the same spot. The speed of boat in still water is 12 km per hour.Find the speed of water current.

Answer 1

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.