Question

Pratik takes 8 hours to travel 36 km downstream and 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 the speed of water current = x km/h

Speed of boat in still water = 12 km/h

Speed upstream =  (12 − x) km/h

Speed downstream = (12 + x) km/h

Distance travelled = 36 km downstream and 36 km upstream 

Total time taken by Pratik = 8 hrs

`"Speed" = "Distance"/"Time"`

∵ `"Time" = "Distance"/"Speed"`

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))/((12 + x)(12 - x))] = 2`

`⇒ 9[(12 - x + 12 + x)/(144 - x^2)] = 2`

`⇒ 9 × 24/(144 - x^2) = 2`

`⇒ 9 × 24 = 2(144 - x^2) `

`⇒ (9 × 24)/2 = 144 - x^2 `

`⇒ 9 × 12 = 144 - x^2 `

`⇒ 108 = 144 - x^2 `

`⇒ x^2 = 144 - 108`

`=> 9 xx 24 = 2 (144 - x^2)`

`=> 9 xx 12 = 144 - x^2`

`=> 144 - 108 = - x^2`

`=> x^2 = 36`

`=> x = +- 6` , but speed ≠ negative

so , x = 6 km/h

Hence, speed of water current is 6 km/h