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The Thomas family and the Chen family each used their sprinklers last summer. The water output rate for the Thomas family's sprinkler was 30 L per hour. The water output rate for the Chen family's sprinkler was 40 L per hour. The familles used their sprinklers for a combined total of 35 hours, resulting in a total water output of 1200 L. How long was each sprinkler used?​

User LanDenLabs
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Answer:

Explanation:

Let's call the amount of time (in hours) that the Thomas family used their sprinkler "t" and the amount of time (in hours) that the Chen family used their sprinkler "c".

We know that the total amount of time the sprinklers were used is 35 hours, so we can write an equation:

t + c = 35 (Equation 1)

We also know that the total water output was 1200 L. To find the amount of water each family used, we need to use the water output rate and the amount of time each family used their sprinkler. For example, the amount of water the Thomas family used can be calculated as:

30t (L of water)

Similarly, the amount of water the Chen family used can be calculated as:

40c (L of water)

The total amount of water used by both families is 1200 L, so we can write another equation:

30t + 40c = 1200 (Equation 2)

Now we have two equations with two unknowns (t and c), which we can solve simultaneously.

One way to do this is to solve Equation 1 for one of the variables (for example, t) and substitute it into Equation 2. We get:

t = 35 - c (from Equation 1)

30t + 40c = 1200 (from Equation 2)

Substituting t = 35 - c into the second equation, we get:

30(35 - c) + 40c = 1200

Expanding and simplifying, we get:

1050 - 30c + 40c = 1200

10c = 150

c = 15

So the Chen family used their sprinkler for 15 hours.

We can substitute this value back into Equation 1 to find the amount of time the Thomas family used their sprinkler:

t + c = 35

t + 15 = 35

t = 20

So the Thomas family used their sprinkler for 20 hours.

Therefore, the Thomas family used their sprinkler for 20 hours and the Chen family used their sprinkler for 15 hours.

User Sushicutta
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