Question

.a motor boat takes 2 hours more to cover a distancef 30 km upstream than it takes to cover the same distance downstream if the speed of the stream is 2km/hr,find the speed of the boat in still water

Answer 1

let the time taken to cover a distance of 30 km be x and then the time taken by up stream will be x+2
speed of downstream = 30/x
speed of upstream = 30/x+2
speed of the stream = (downstream - upstream)/2
2 = (30/x-30/x+2)/2
=> 4 = (30(x+2) -30(x) )/x(x+2)
4(x(x+2)) = 30(x+2-x)
4(x^2 + 2x) = 60
4x^2 + 8x - 60 =0
divide the above equation by 4

x^2 +2x - 15 =0
factorising the equation we get
(x+5)(x-3)=0
x= -5 x= 3
avoiding negative we have the x = 3
the x +2 = 5
Speed of the boat in still water = (downstream+upstream)/2
= (30/3+ 30/5)/2
= (10+6)/2
=16/2
=8 km/hr