OSYSTEMS OF EQUATIONS AND MATRICESМаxSolving a value mixture problem using a system of linear equationsEspañolThe Howard family and the Patterson family each used their sprinklers last summer. The water output rate for the Howard family's sprinkler was 35 L per hour.The water output rate for the Patterson family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in atotal water output of 1475 L. How long was each sprinkler used?Note that the ALEKS graphing calculator can be used to make computations easier.Howard family's sprinkler:hours?Patterson family's sprinkler:hoursАа

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Asked Oct 9, 2019
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OSYSTEMS OF EQUATIONS AND MATRICES
Маx
Solving a value mixture problem using a system of linear equations
Español
The Howard family and the Patterson family each used their sprinklers last summer. The water output rate for the Howard family's sprinkler was 35 L per hour.
The water output rate for the Patterson family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a
total water output of 1475 L. How long was each sprinkler used?
Note that the ALEKS graphing calculator can be used to make computations easier.
Howard family's sprinkler:
hours
?
Patterson family's sprinkler:
hours
Аа
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OSYSTEMS OF EQUATIONS AND MATRICES Маx Solving a value mixture problem using a system of linear equations Español The Howard family and the Patterson family each used their sprinklers last summer. The water output rate for the Howard family's sprinkler was 35 L per hour. The water output rate for the Patterson family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1475 L. How long was each sprinkler used? Note that the ALEKS graphing calculator can be used to make computations easier. Howard family's sprinkler: hours ? Patterson family's sprinkler: hours Аа

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Expert Answer

Step 1

Let Howard’s family sprinkler used for x hours and Patterson family’s sprinkler used for y hours.

It is given that, total combined time used is 55 hours, therefore we will have:

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x+y55 (1)

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Step 2

Also, it is given that water output rate for Howard’s family sprinkler is 35L per hour and 20L per hour for Patterson family’s sprinkler and total water output is 1475L, therefore:

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35x 20y 1475 (2)

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Step 3

Now, to solve multiply (1) by 20 ...

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15x 375 x = 25

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