Problema Solution
The Kelly family and the Rogers family each used their sprinklers last summer. The water output rate for the Kelly family's sprinkler was 15L per hour. The water output rate for the Rogers family's sprinkler was 30 L per hour. The families used their sprinklers for a combined total of 70 hours, resulting in a total water output of 1500 L . How long was each sprinkler used?
Answer provided by our tutors
Let
't1' be the time that the Kelly family used their sprinkle then the total amount of their total output is 15*t1 L
't2' be the time that the Rogers family used their sprinkle then the total amount of their total output is 30*t2 L
We need to find t1 and t2.
The families used their sprinklers for a combined total of 70 hours:
t1 + t2 = 70
We also know that the total output is 1500 L that is
15*t1 + 30*t2 = 1500 divide both sides by 15
t1 + 2*t2 = 100
From t1 + t2 = 70 we have t1 = 70 - t2 and substituting in t1 + 2*t2 = 100 we get
70 - t2 + 2*t2 = 100
- t2 = 100 - 70
- t2 = -30 multiply both sides by (-1)
t2 = 30 hours
t1 = 70 - t2
t2= 70 - 30
t2 = 40 hours
The Kelly family used their sprinkle for 20 hours. The Rogers family used their sprinkle for 40 hours.