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.
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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
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