Solving for the Robinson family and Alexander family

Question

The Robinson family and the Alexander family each used their sprinklers last summer. The water output rate for the Robinson family's sprinkler was 15 L per hour. The water output rate for the Alexander familys sprinkler was 35L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1450L. How long was each sprinkler used

Answer 1

Ashley,

 

We can solve this problem by setting up 2 equations with 2 unknowns which are the times each sprinkler was used.

 

Let's assume that:

x = number of hours that the Robinson sprinkler was used

y = number of hours that the Alexander sprinkler was used

 

The problem tells us that both sprinklers were on for a total of 50 hours. So that means that:

x + y = 50

 

The problem also tells us that the Robinson sprinkler flow rate is 15L/hr and the Alexander sprinkler flow rate is 35L/hr. It also states that the total amount of water used is 1450L.

Because the water used by each sprinkler is equal to the flow rate times the time that each was on, we can make the following equation:

(15) (x) + (35) (y) = 1450

 

Now we have 2 equations for x and y and can now solve for them.

We can do this by solving for x in the first equation and then plugging that value into the second equation and solve for y. Once we know y, we can then get x.

 

From the first equation: x = 50 - y

Plugging this value of x into the second equation gives:

(15) (50-y) + (35) (y) = 1450

Solve for y:

750 - 15y + 35y = 1450

Get all the y's on one side of the equation.

20y = 700

y = 35

We know that x = 50 - y so x then is 15.

 

So that means the Robinson sprinkler was on for 15 hours and the Alexander sprinkler was on for 35 hours.

 

Hope this helps!