Let the larger tap take x hours to fill the tank completely.
∴ Part of tank filled by the larger tap in 1 hour = 1/x
Also, the smaller tap takes (x + 3) hours to fill the tank completely.
∴ Part of tank filled by the smaller tap in 1 hour = 1/(x + 3)
∴Part of tank filled by both the taps in 1 hour
\(=(\frac{1}{x} + \frac{1}{x + 3})\)
But, the tank gets filled in 2 hours by both the taps.
∴ Part of tank filled by both the taps in 1 hour = 1/2
According to the given condition,
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
∴ x – 3 = 0 or x + 2 = 0
∴ x = 3 or x = -2
But, time cannot be negative.
∴ x = 3 and x + 3 = 3 + 3 = 6
∴ The larger tap takes 3 hours and the smaller tap takes 6 hours to fill the tank completely.