Question

The Harris family and the Baker family each used their sprinklers last summer. The water output rate for the Harris family's sprinkler was 20L per hour. the water output rate for the Baker family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 75 hours, resulting in a total water output of 2025L. How long was each sprinkler used?

Answer 1

Answer:40 hr and 35 hr

Explanation:

Given

Harris family sprinkler output rate is
`20\ L/\text{per hour}`

and Baker family sprinkler output rate is
`35\ L/\text{per hour}`

Total output of two is
`2025\ L`

Suppose Harris family sprinkler used for
`t_1` time and Baker family for
`t_2`time then

`20* t_1+35* t_2=2025\quad \ldots(i)`

and
`t_1+t_2=75`

`t_1=75-t_2`

Substitute the value in
`(i)`

`\Rightarrow 20* (75-t_2)+35t_2=2025`

`\Rightarrow 1500-20t_2+35t_2=2025`

`\Rightarrow 15t_2=525`

`\Rightarrow t_2=(525)/(15)`

`\Rightarrow t_2=35\ hr`

`\therefore \ t_1=75-35=40\ hr`

Therefore Harris family use
`40\ hr` of sprinkler and Baker family use
`35\ hr` of sprinkler