Question

a motor boat went down stream for 350 km and immidiately returned .it took the boat 16 hours to complete the round trip. if the speed of the 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

Answer:

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

Step-by-step explanation: