Question

a hose with a larger diameter working alone can fill a swimming pool in 9 hours. a hose with a smaller diameter working alone can fill a swimming pool in 18 hours. working together, how long would it take the two hoses to fill the swimming pool? the rate of the hose with the large diameter is 1/9 1/18 1/27 done

Explanation:

Step1: Determine the filling rate of each hose

The rate of work is the fraction of the job done per unit of time. If a hose with a larger diameter can fill a swimming - pool in 18 hours, then its rate of filling the pool is $\frac{1}{18}$ of the pool per hour. If a hose with a smaller diameter can fill a swimming - pool in 9 hours, then its rate of filling the pool is $\frac{1}{9}$ of the pool per hour.

Step2: Calculate the combined rate of the two hoses

When two hoses work together, their combined rate is the sum of their individual rates. Let $r_1=\frac{1}{18}$ (rate of the larger - diameter hose) and $r_2 = \frac{1}{9}$. Then the combined rate $r=r_1 + r_2=\frac{1}{18}+\frac{1}{9}=\frac{1 + 2}{18}=\frac{3}{18}=\frac{1}{6}$ of the pool per hour.

Step3: Find the time taken to fill the pool together

We know that rate $r=\frac{1}{t}$, where $t$ is the time taken to complete the job. Since $r=\frac{1}{6}$, then $t = 6$ hours.

Answer:

6 hours