Question

The Murphy family and the Jenkins family each used their sprinklers last summer. The water output rate for the Murphy family's sprinkler was 40L per hour. The water output rate for the Jenkins family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of hours 45L, resulting in a total water output of 1900L. How long was each sprinkler used?

Answer 1

Murphy family used their sprinkler for 20 hours and Jenkins family used their sprinkler for 25 hours.

Explanation:

Let Murphy family used sprinkler for x hours and Jenkins family used the sprinkler for y hours.

Since water output rate of Murphy's family sprinkler was 40 L per hour

So in x hours amount of water collected = 40x L

Similarly water output of Jenkins family sprinkler was 35L per hour.

So in y hours amount of water collect = 35y L

Now the resulting amount of water was 1900 L

Therefore, equation representing the total amount of water will be

40x + 35y = 1900

Or 8x + 7y = 380 --------(1) [ divide the equation by 5]

Total time consumed = 45 hours

So another equation will be

x + y = 45 --------(2)

Now multiply the equation 2 by 8 and subtract equation 1

8(x + y) - (8x + 7y) = 380 - 8.(45)

(8x - 8x) + (8y - 7y) = 380 - 360

y = 20 hours

Now we put x = 20 in equation 2

20 + y = 45

y = 45 - 20

y = 25

Therefore, Murphy family used their sprinkler for 20 hours and Jenkins family used their sprinkler for 25 hours.