value mixture problem

Question

The Martin family and the Barnes family each used their sprinklers last summer. The Martin family's sprinkler was used for 25 hours. The Barnes family's sprinkler was used for 40 hours. There was a combined total output of 1475 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour?

Answer 1

I would do a system of equations for this type of problem.

First let's make the equation for the amount of water used. Since it does not matter what the variables are, I will use M for the Martin Family and B for Barnes family.

According to the problem, will will connect the number of hours with the family variable to equal the total amount of water used by the families.

25M + 40B = 1475

Now, let's create an equation for the flow rate of both families.

M + B = 50

Now, I will create an equation that can be substituted in the original equation to find the flow rate of one of the families.

M + B = 50

M = 50 - B

Now substitute this equation in the original equation.

25 (50-B) + 40B = 1475

1250 - 25B + 40B = 1475

1250 + 15B = 1475

1250 + 15B -1250 = 1475 -1250 (keep your equation balanced by subtracting from both sides)

15B = 225

15B/15 = 225/15

B = 15

M= 50 - 15

M = 35

Now you can double check your answers by substituting the solutions into the original equations.

25M + 40B = 1475

25 (35) + 40 (15) = 1475

875 + 600 = 1475

1475 = 1475

{I recommend double checking your answer because when I did the final part of the problem and was not getting the correct answers, I found that I had accidentally typed in one number wrong and because I carried that wrong number through the rest of the equation, I did not have the correct answer in the end.}

Answer 2

Let x = rate (in liters per hour) for the Martin's sprinkler

Let y = rate (in liters per hour) for the Barnes' sprinkler

Then, x + y = 50 and 25x + 40y = 1475

So, -25x - 25 y = -1250 and 25x + 40y = 1475

Add the equations to obtain 15y = 225

Therefore, y = 15 liters per hour and x = 35 liters per hour,