Question

Two hoses are pouring water into an empty pool. Hose $1$ alone would fill up the pool in $6$ hours. Hose $2$ alone would fill up the pool in $4$ hours. How long would it take for both hoses to fill up two-thirds of the pool?

• A. $2\frac{4}{5}$ hours
• B. $3\frac{4}{5}$ hours
• C. $2\frac{3}{5}$ hours
• D. $1\frac{3}{5}$ hours

Answer 1

Answer: (D)

$1\frac{3}{5}$ hours

If Hose $1$ can fill the pool in $6$ hours, its are $\frac{1}{6}$ 'pool per hour,' or the fraction of the job it can do in one hour. Likewise, if Hose $2$ can fill the pool in $4$ hours, its rate is $\frac{1}{4}$ pool per hour. Therefore, the combined rate is $\frac{5}{12}$ pool per hour $(\frac{1}{4}+\frac{1}{6}=\frac{5}{12})$:

$RT=W$

$\left(5/12\right)t=2/3$

$t=\left(\frac{2}{3}\right)\left(\frac{12}{5}\right)=\frac{8}{5}=1\frac{3}{5}$ hours.