Question

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The Alexander family and the Anderson family each used their sprinklers last summer. The Alexander family's sprinkler was used for 30 hours. The Anderson family's sprinkler was used for 20 hours. There was a combined total output of 1450L of water. What was the water output rate for each sprinkler if the sum of the two rates was 55L per hour?

Answer 1

`\large \boxed{\text{35 gal/min and 20 gal/min}}`

Explanation:

Let x = the Alexander flow rate

and y = the Anderson flow rate

You have two conditions:

`\begin{array}{lccc}(1) & 30x + 20 y & = & 1450 \\(2) & x + y & = & 55\\\end{array}`

Solve the equations for x and y

`\begin{array}{rccrl}(3)\qquad \qquad\qquad \quad y & = & 55 - x & \text{Subtracted x from each side of (2)}\\\30x + 20(55 - x)& = &1450 &\text{Substituted (3) into (1)}\\30x +1100 - 20x & = &1450 &\text{Distributed the 20}\\10x + 1100 & = & 1450 & \text{Simplified}\\10x & = &350&\text{Subtracted 1100 from each side} \\\end{array}\\`

`\begin{array}{rcrl}(4) \qquad \qquad\qquad \quad x & = &\mathbf{35}&\text{Divided each side by 10} \\35 + y & = &55&\text{Substituted (4) into (2)} \\y & = &\mathbf{20}&\text{Subtracted 35 from each side2} \\\end{array}\\\text{The Alexander and Anderson sprinkler flow rates are}\\\large \boxed{\textbf{35 gal/min and 20 gal/min}}`

Check:

`\begin{array}{rcrl}30(35) +20(20)= 1455 & \qquad & 35 + 20 = 55\\1050 + 400 =1450 & \qquad & 55 = 55\\1450 = 1450& \qquad &\\\end{array}`

OK.