Question

Two taps running together can fill a tank in 40/13 hours. If one tap tales 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?

Answer 1

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Answer 2

Hi Harsha !

Let the smaller diameter tap takes x hours to fill the tank

Then, time taken by larger diameter tap to fill the tank=(x-3)

Both taps together can fill the tank in 40/13 hours 

portion of tank filled by smaller diameter tap in x hours= 1/x

portion of tank filled by smaller diameter tap in40/13  hours= 40/13x



portion of tank filled by larger diameter tap in (x-3) hours=1/x-3

portion of tank filled by larger diameter tap in 40/13 hours= 40/13(x-3)

ATQ,
40/13x+40/13(x-3)=1

1/x+1/x-3=13/40

x-3+x/x(x-3)=13/40
 
2x-3/x²-3x=13/40

13x-119x+120=0
a=13
b=119
c=120
D=b²-4ac
  =14161-6240
  =7921
applying quadratic formula we get two roots = -b+√D/2a and -b-√D/2a
119+89/26 and 119-89/26
8   and 15/13 
x= 15/13 neglected because time taken by smaller tap cannot be less than 3 hours
so smaller tap time = 8 hours and larger tap = 5 hours
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