Math Question

Question

The Cooper family and the Young family each used their sprinklers last summer. The water output rate for the Cooper family's sprinkler was 40L per hour. The water output rate for the Young family's sprinkler was 30L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total output of 2300L. How long was each sprinkler used?

Answer 1

The trick here is to set up two equations with two unknowns, so how do you figure out the two equations?

 

So let     C = the # of hours the Coopers used their sprinklers.

and let   Y = the # of hours the Youngs used their sprinklers.

 

So you know the total water use has to equal:    (number of hours) x (use per hour). So if you add this up for each family, it will be the total used = 2300. so:

 

40C + 30Y = 2300

 

Then you also know that the total hours was 65 so

 

C+Y =65    or rearrange to C = 65-Y.

 

Then just plug (65-Y) into 'C' in the first equation to solve for Y. Then once you know Y, use either equation to solve for C.