Question

Two taps running together can fill a tank in 3 1/13 hours. If one tap takes
3 hours more than the other to fill the tank, then how much time will
cach tap take to fill the tank?​

Answer 1

Answer:

5 hrs, 8 hrs respectively.

Step-by-step explanation:

Let x be time taken by 1 tap.

Time taken by second tap = x + 3

Two taps running together will fill in 1 hr  = 1/x + 1/x +3 = 2x+3/x(x+3)

But it is given they fill the tank in 3 1/13 hrs = 40/13 hrs.

In 1 hr they together fill 13/40 part.

2x+3/x(x+3) = 13/40

=> 80x + 120 = 13x² + 39

=> 13x² - 41x - 120 = 0

x = 41 ± √(41)² - 4 (13)(-120) / 2 *13 = 1/26(41 ± 89)

=> x = 1/26(41+89) or x = 1/26(41-89)

=> x =  5 or -24/13.

Since x cannot be negative,

The time taken by single tap = 5 hrs.

The time taken by other tap = 8 hrs.