Question

A motor boat shoes speed is 20km per hour in still water takes 1 hour more to go 48 kilometre upstream then to return downstream to the same spot find the speed of stream.

Answer 1

Given:

Speed of boat = 20km/hr

Let speed of stream = x km/hr

We know that

Speed = Distance/time

So, Time(T) = Distance / Speed

Downstream

T = 48/20+x (1)

Upstream

T+1=48/20-x (2)

Putting (1) in (2)

48/20+x + 1 =48/20-x

48/20-x - 48/20+x=1

48(20+x)-48(20-x)/(20+x)(20-x)=1

48[ (20+x)-(20-x)]/20^2 - x^2 =1

{(a+b)(a-b)= a^2-b^2}

48[20+x-20+x]/400-x^2=1

48[2x]/400-x^2=1

96x=400-x^2

x^2+96x-400=0

b^2-4ac

(96)^2-4(1)(-400)

9216+1600

10816>0 [ roots exist ]

Applying quadratic formula

x= -b+- √ b^2-4ac/2a

-96+- √10,816/2

-96+- √ (104)^2/2

-96 +- 104/2

x=-96-104/2 = -100km/hr (omitted)

Or

x=-96+104/2 = 4km/hr

Therefore speed of stream is 4km/hr