Two water taps together can fill a tank 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.?

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Answer

Answer

25 hours taken by the smaller diameter of the tap and 15 hours taken by the bigger diameter of the tap to fill the tank

Answer

**Given data:**
- The time taken by two taps together to fill the tank is 9 and 3/8 hours.
- The tap with the larger diameter takes 10 hours less than the tap with the smaller diameter to fill the tank separately.

**Let's assume:**
- The time taken by the tap with the smaller diameter to fill the tank separately is 'x' hours.
- The time taken by the tap with the larger diameter to fill the tank separately is 'x - 10' hours.

**Calculation:**
- The combined efficiency of the two taps is given by the formula:
Efficiency = (Product of individual efficiencies) / (Sum of individual efficiencies)

- Let's assume the efficiency of the tap with the smaller diameter is 'E1' and the efficiency of the tap with the larger diameter is 'E2'.
- The efficiency of a tap is inversely proportional to the time taken to fill the tank.
- Therefore, the efficiency of the tap with the smaller diameter is 1/x and the efficiency of the tap with the larger diameter is 1/(x-10).

- The combined efficiency of the two taps is given by:
E = (1/x) + (1/(x-10))

- The time taken by the two taps together is given by the formula:
Time = (Product of individual times) / (Sum of individual efficiencies)

- Substituting the given values into the formula, we get:
9 and 3/8 hours = (x*(x-10)) / (x + (x-10))

- Solving this equation for x, we get:
9 and 3/8 hours = (x^2 - 10x) / (2x - 10)
9 and 3/8 hours * (2x - 10) = x^2 - 10x
(75/8)*(2x - 10) = x^2 - 10x
(75/4)*(x - 5) = x^2 - 10x
75x - 375 = 4x^2 - 40x
4x^2 - 115x + 375 = 0

- Solving this quadratic equation, we find the values of x, which represent the time taken by the tap with the smaller diameter to fill the tank separately.

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