Suppose, first pipe alone takes
x hours to fill the tank .
Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
∴ |
1 |
+ |
1 |
= |
1 |
x |
(x - 5) |
(x - 9) |
⟹ |
x - 5 + x |
= |
1 |
x(x - 5) |
(x - 9) |
⟹ (2x - 5)(x - 9) = x(x - 5)
⟹ x2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
⟹ x = 15. [neglecting x = 3]