The Kim family and the Washington family each used their sprinklers last summer. The water output rate for the Kim family's sprinkler was 15L per hour. The water output rate for the Washington family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?

Question

Mathematics

Nigel Ho

20 January, 06:14

The Kim family and the Washington family each used their sprinklers last summer. The water output rate for the Kim family's sprinkler was 15L per hour. The water output rate for the Washington family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?

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Answers (1)

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Taco · Answer 1

Correct answer: Kim family x = 30 hours and Washington family y = 35 hours

Step-by-step explanation:

We will first define unknown variables:

Let Kim family time be x and Washington family time be y

We will solve this problem using the following system.

15 x + 40 y = 1850 and

x + y = 65

we will multiply the second equation by the number - 15 and add by the first and we will get:

15 x + 40 y = 1850

- 15 x - 15 y = - 15 · 65 = - 975

25 y = 875 ⇒ y = 875/25 = 35

y = 35 hours

x = 65 - y = 65 - 35 = 30 hours

x = 30 hours

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