Question

It takes two water hoses 1 hour and 20 minutes to fill a pool. It takes the smaller hose 2 hours more to fill the pool than the larger one. How long will it take to fill the pool if only the large hose was available?

Answer 1

If only the large hose was available, it would take 1 hour to fill the pool.

Step-by-step explanation:

To solve this problem, let's assume that the larger hose takes x hours to fill the pool. Since it takes 2 hours more for the smaller hose to fill the pool, the smaller hose would take x + 2 hours to fill the pool.

Using the concept of work rate, we can set up the equation: 1 / (x) + 1 / (x + 2) = 1 / (1 hour and 20 minutes).

Simplifying the equation, we get: (2x + 2) / (x^2 + 2x) = 1 / (4/3).

Cross-multiplying and simplifying further, we get: 3(2x + 2) = 4(x^2 + 2x).

Expanding and rearranging the equation, we get: 6x + 6 = 4x^2 + 8x.

Simplifying further, we get: 4x^2 + 2x - 6 = 0.

Using the quadratic formula to solve for x, we get: x = (-2 ± sqrt(2^2 - 4(4)(-6))) / (2(4)).

Simplifying further, we get: x = (-2 ± sqrt(4 + 96)) / 8.

Calculating the square root, we get: x = (-2 ± sqrt(100)) / 8.

Simplifying further, we get: x = (-2 ± 10) / 8.

Using both solutions, we have: x = (-2 + 10) / 8 = 8/8 = 1; x = (-2 - 10) / 8 = -3/2 = -1.5.

Since we can't have a negative value for time, the larger hose would take 1 hour to fill the pool if only it was available.