s for a combined total of 45 hours, resulting in a total water output of 1600L . How long was each sprinkler used?

Question

The water output rate for the Washington family's sprinkler was 30L per hour. The water output rate for the Richardson family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1600L . How long was each sprinkler used?

Answer 1

• The # of hours used by the Washington sprinkler + The number of hours used by the Richardson sprinkler = 45
• Let X = The # of hours used by the Washington sprinkler
• Let (45 - X) =  The number of hours used by the Richardson sprinkler
• This should make sense because the number of hours used by the Washington sprinkler + The number of hours used by the Richardson sprinkler = 45, and X + (45 - X) = 45
• Water Output = (Output Rate per hour) (The # of hours used by the sprinkler)
• Washington Water Output = (30L/Hr)(X) = 30X
• Richardson  Water Output = (40L/Hr)(45 - X) = 1800 - 40X
• It is stated in the problem that the Washington water output + the Richardson water output = 1600 L
• Hence, 30X + 1800 - 40X = 1600
• Solving for X, I get -10X = -200, ergo, X = 20.
• As stated in the second line of the solution,  X = The # of hours used by the Washington sprinkler, so the Washington sprinkler is used for 20 Hours.
• As stated in the third line of the solution, (45 - X) = The number of hours used by the Richardson sprinkler.
• Since X = 20, (45 - X) = 45 - 20 = 25 Hours. The # of hours used by the Richardson sprinkler is 25.