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Question

Two taps running together can fill a tank in 3 113 hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?


Solution

Let time taken by 1st tap to fill the tank = x hrs

Time taken by 2nd tap = (x+3) hrs

Together they fill in 3113=4013hrs

Now,

1x+1x+3=1340

x+3+x(x)(x+3)=1340

2x+3x2+3x=1340

13x2+39x=80x+120

13x241x120=0 13x265x+24x120=0

13x(x5)+24(x5)=0

(x5)(13x+24)=0

Either x5=0or13x+24=0

x=5,x=2413[Rejected]
 So, 1st tap fill the tank in 5 hrs

and  2nd tap fill the tank in 5 + 3 = 8 hrs

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