Question

15. A tank fills completely in 2 hours if both the taps are open. If
only one of the taps is open at the given time, the smaller tap
takes 3 hours more than the larger one to fill the tank. How much
time does each tap take to fill the tank completely ?
​

Answer 1

Step-by-step explanation:

larger tape take x hours

then smaller tape takes x+3 hours

together they are take

1/x +1/x+3=1/2

2x+3/x^2+3x=1/2

4x+6=x^2+3x

x^2-x-6=0

x^2-3x+2x-6=0

x(x-3)+2(x-3)=0

(x-3)(x+2)=0

x=3

larger tape take 3hours

smaller tape take 6hours