Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool. PLEASE HELP! I will make you brainlist if you solve and tell me the answer!
Answers
Answer: 1 hour 40mins= 100mins
Step-by-step explanation:
Let,
L: flow rate of large pump
S: flow rate of small pump
So we can write 3 expressions as:
(2L+1S) × 4hrs=swimming pool volume
(1L+3S)× 4hrs= swimming pool volume
(4L+4S) × x hrs.=swimming pool volume
We write a system of 3 equations, with x, L and S as variables:
exp1=exp2
exp2=exp3
exp3=exp1
then:
4(2L + S) =4 (L + 3S)
4(L+3S)= (4L+4S)x
(4L+4S)x=4(2L+S)
From eqn 1 we obtain:
L=2S
Substituting L in the other equations and collecting terms, we get:
20S=12Sx
12Sx=20S
x = 20/12=5/3 =1 hour 40mins= 100mins
We get the same equation twice, which means the system is inconsistent and there’s no unique solution. Dividing by S, we finally get:
x = 20/12=5/3 =1 hour 40mins= 100mins
Conclusion: The solution does not depend on the pumps or swimming pool sizes, only on the ratio of L to S.