Question

Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boats in still water is 12km. Per hour. Find the speed of water current.

Answer 1

let speed of water current be x kmph
downstream speed of boat 12+x kmph
upstream speed 12-x kmph
$\frac{36}{12 - x} + \frac{36}{12 + x} = 8 \\ \frac{9}{12 - x} + \frac{9}{12 + x} = 2 \\ \frac{9(12 + x) + 9(12 - x)}{(12 + x)(12 - x)} = 2 \\ \frac{108 + 9x + 108 - 9x}{144 - {x}^{2} } = 2 \\ \frac{216}{144 - {x}^{2} } = 2 \\ 216 = 2(144 - {x}^{2} ) \\ 108 = 144 - {x}^{2} \\ 108 - 144 = - {x}^{2} \\ - 36 = - {x}^{2} \\ {x}^{2} = 36 \\ x = \sqrt{36 } \\ x = 6$
speed of water current is 6 kmph