Question

pratik takes 8 hour to travel 36km downstream and return to the same spot. The speed of boat in still water is 12km/hr.find the speed of water current
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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/hr

Answer 2

speed of boat in still water = 12 km/h

let speed of water current be = x km/h

A.T.Q,

(36/12+x) + (36/12-x)=8

36x -12(36) + 36x + 36(12)/12^2-x^2=8

72x/-x^2+144=8

Divide by 8 both sides

9x=144-x^2

x^2+9x-144=0