Question

i. 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:

Let the larger tap take x hours

Smaller tap takes x+3hours

Both fill the tank in 2hours if they are open together

Amount of water filled by larger tap in 1hour=1/x

Amount of water filled by smaller tap in 1 hour=1/x+3

Amount of water filled in 2hours=1/2

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

= 2x+3/x2+3x=1/2

=4x+6=x2+3x

=x2-x-6=0

=x2-3x+2x-6=0

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

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

=x=3 , -2

Thus the larger tap takes 3 hours while the smaller tap takes 3+3=6hours