math help please

Question

The Simmons family and the Taylor family each used their sprinklers last summer. The Simmons family's sprinkler was used for 20

 hours. The Taylor family's sprinkler was used for 15

 hours. There was a combined total output of 1100L

 of water. What was the water output rate for each sprinkler if the sum of the two rates was 65L

 per hour?

Answer 1

The rate of water used = amount of water used divided by the time used.

Since the total amount of water used was 1100 L, we can say the Simmons used "x" amount of water and the Taylors used "1100 - x".

So the rate that the Simmons family's sprinklers ran at would be x/20. And we can say the rate that the Taylor family's sprinklers ran at was (1100 - x)/15..

We are told that the sum of the 2 rates is 65 L/hr so we can say x/20 + (1100 - x)/15 = 65

Using a common denominator of 300, we can say:

15x/(15•20) + 20(1100 - x)/(20•15) = 65

15x/300 + (22000 - 20x)/300 = 65

15x + 22000 - 20x = 65(300)

-5x = 65(300) - 22000

-5x = -2500

x = 500 L (again this is the amount of water the Simmons' used). Then the amount of water the Taylor's used would be 1100 - 500 = 600 L

The rate of the Simmons' sprinklers would then be 500/20 = 25 L/hr

The rate of the Taylor's sprinklers would be 600/15 = 40 L/hr