Four large and 2 small pumps can fill a swimming pool in 2 hours. Two large and 6 small pumps can also fill the same swimming pool in 2 hours. How long does it take 8 large and 8 small pumps to fill 50% of the swimming pool. (NOTE: all the large pump have same power and all the small pumps have the same power).

Guest Jan 28, 2019

#2**+2 **

x=small pump rate y = large pump rate

4y + 2x = Swimming pool (in 2 hours) = 1 pool/2hr

AND:

2 y + 6x = swimming pool (in 2 hours) = 1 pool/2hr

From the first equation 2x = 1/2 - 4y

x = 1/4-2y substitute this into the second equation

2y + 6 ((1/4-2y) = 1/2 Solve for y

2y + 6/4 -12y = 1/2

-10y = -1

y = 1/10 pool/ hr Sub this into 1st(or 2nd) equation:

4(1/10) + 2x = 1/2 solve for x = 1/20 pool/hr

Now : for the final part of the question.....

( 8(y) + 8(x)) t = 1/2 pool

( 8(1/10) + 8(1/20) ) t = 1/2

(16/20 + 8/20) t = 1/2

( 24/20 ) t = 1/2

t = 1/2 * 20/24 = 20/48 hr = 20/48*60 = 25 mins

ElectricPavlov Jan 28, 2019

#3**+2 **

**4L + 2S =2L + 6S, solve for L L = 2S - This means the capacity of 1 large pump = 2 small pumps. 4L + 2S = Equivalent to 5 Large pumps in capacity. 8 Large pumps + 8 Small pumps = Equivalent in Capacity to 8+4 = 12 Large pumps. 12 large pumps / 5 Large pumps = 2 2/5 times - filling capacity of 8 Large and 8 small pumps. Therefore it takes: 120 minutes / (12/5) =50 - minutes to fill the pool. 50/2 =25 minutes to fill 50% of the pool.**

Guest Jan 28, 2019

edited by
Guest
Jan 28, 2019

#4**+1 **

Let (1/x) be the amount of the pool filled by a large pump in 1 minute

Let (1/y) be the amount of the pool filled by a small pump in one minute

So we have this system

4(1/x)(120) + 2(1/y)(120) = 1 ⇒ 480/x + 240/ y = 1 (1)

2(1/x)(120) + 6(1/y)(120) = 1 ⇒ 240/ x + 720/y = 1 ⇒ -480/x - 1440/ y = -2 (2)

Add (1) and (2)

-1200/ y = - 1 ⇒ y = 1200

And

480/x + 240/1200 = 1

480/x + 1/5 = 1

480/x = 4/5

x/480 = 5/4

x = 480 (5/4) = 600

So.....the large pump fills 1/600 of the pool in a minute and the small pump fills 1/1200 pool every minute

So....in each minute they filll 1/400 of the pool working together

So.....8 times this = 8/400 of the pool = 1/50 of the pool

So..... (1/50) * minutes = 1/2

Minutes = 50/2 = 25 minutes

CPhill Jan 29, 2019