Question

The Collins family and the Watson family each used their sprinklers last summer. The Collins family's sprinkler was used for 20 hours. The Watson family's sprinkler was used for 25 hours. There was a combined total output of 875L of water. What was the water output rate for each sprinkler if the sum of the two rates was 40L per hour?

Answer 1

Collins: 25 L/h

Watson: 15 L/h

Step-by-step explanation:

Collins family:

Hours: Hc = 20 h

Water used: Wc

Rate: Rc = Wc/Hc

Watson family:

Hours: Hw = 25 h

Water used: Ww

Rate: Rw = Ww/Hw

Total output = Wc + Ww = 875 L

Sum of rates: Rt = Rc + Rw = 40 L/h

`Rt = (Wc)/(Hc) + (Ww)/(Hw)`

`Rt = (Wc)/(Hc) + (Wt - Wc)/(Hw) \\Rt = (HwWc + HcWt - HcWc)/(HcHw) \\RtHcHw = HwWc - HcWc + HcWc\\RtHcHw = (Hw-Hc)Wc + HcWt\\Wc = (RtHcHw - HcWt)/(Hw-Hc) \\\\Wc = (40 x 20x25 - 20x875)/(25-20) \\\\Wc = 500 L\\\\Ww = 875 - 500 = 375L\\\\Rc = (500)/(20)  = 25 L/h\\\\Rw = (375)/(25)  = 15 L/h`