Question

A garden hose can fill a swimming pool in 7 days, and a larger hose can fill the pool in 4 days. How long will it take to fill the pool if both hoses are used?

Answer 1

`2 (6)/(11)\; \rm days\;`

2 days 13 hours 5 minutes 27 seconds

Explanation:

First hose:

• If the first hose can fill the pool in 7 days, then it can fill 1/7 of the pool in 1 day.

Second hose:

• If the second hose can fill the pool in 4 days, then it can fill 1/4 of the pool in 1 day.

When both hoses are being used to fill the pool, their rates are additive:

`\implies (1)/(7)+(1)/(4)=(4)/(28)+(7)/(28)=(11)/(28)`

Therefore, both hoses can fill 11/28 of the pool in 1 day.

To calculate how long it will take to fill the pool, divide 1 day by the combined rate:

`\implies 1 / (11)/(28)=1 * (28)/(11)= (28)/(11)=2 (6)/(11)\; \rm days\;`

Therefore it takes 2 ⁶/₁₁ days to fill the pool if both hoses are used.

To find the time it takes in days, hours, minutes and seconds:

• 6/11 days as hours is:
  
  `\implies (6)/(11) * 24=13(1)/(11)\; \rm hours`

• 1/11 hours as minutes is:
  
  `\implies (1)/(11) * 60=5(5)/(11)\; \rm minutes`

• 5/11 minutes as seconds is:
  
  `\implies (5)/(11) * 60=27.27\; \rm seconds`

Therefore, it takes:

• 2 days 13 hours 5 minutes 27 seconds to fill the pool if both hoses are used (to the nearest second).