Question

A motor boat went downstream for 350 km and immediately returned. it took the boat 16 hours to complete the round trip. if the speed of river was twice the normal, the trip downstream and back would take 20 hours. what is the speed of boat in still water?

Answer 1

speed of boat = x
speed of current = y 

350/(x+y) + 350(x-y) = 16
350(x-y) + 350(x+y) = 16(x^2 - y^2)
700x = 16x^2 - 16y^2 ---(i)

and
350/(x+2y) + 350/(x-2y) = 20
350(x-2y) + 350(x+2y) = 20(x^2 - 4y^2)
700x = 20x^2 - 80y^2 ---(ii)

from 1st and 2nd equation
16x^2 - 16y^2 = 20x^2 - 80y^2
4x^2 = 64y^2
 2x = 8y
   x = 4y ---(iii)

3rd equation put on 1st equation
 700(4y) = 16(4y)^2 - 16y^2
 2800y = 64y^2 - 16y^2
 2800y = 48y^2
         y = 2800/48 = 175/3 = 58.33 km/hr
speed of boat = x = 4y = 4(58.33) = 233.33 km/hr

i hope it will help you
regards

Answer 2

Answer:

$\frac{140}{3} km \: per \: hour$