Question

If two pipes function simultaneously, the reservoir is filled in 6 hours. One pipe fills the reservoir 5 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?

Answer 1

The faster pipe takes 10 hours to fill the reservoir.

Step-by-step explanation:

To solve this problem, we can set up an equation based on the given information. Let's say the faster pipe takes x hours to fill the reservoir. This means the slower pipe takes x + 5 hours to fill the reservoir.

If two pipes function simultaneously, they can fill a reservoir in 6 hours, so their combined rate is 1/6 of the reservoir per hour. The faster pipe's rate is 1/x of the reservoir per hour, and the slower pipe's rate is 1/(x+5) of the reservoir per hour.

Setting up the equation using the rates:

1/x + 1/(x+5) = 1/6

Multiplying through by the common denominator 6x(x+5) gives:

6(x+5) + 6x = x(x+5)

Simplifying and rearranging the equation:

12x + 30 = x^2 + 5x

Bringing all terms to one side:

x^2 + 5x - 12x - 30 = 0

x^2 - 7x - 30 = 0

Factoring the quadratic equation:

(x - 10)(x + 3) = 0

So, the possible values for x are x = 10 (which would make the slower pipe take 10 + 5 = 15 hours) or x = -3 (which is not possible in this context since time cannot be negative).

Therefore, the faster pipe takes 10 hours to fill the reservoir.