2 water Pipes fill a tank in 8.40hrs.small pipe take 2.5 hrs longer than big pipe. how Long does big pipe take

Question

2 water Pipes to fill a tank in 8.40hrs.small pipe take 2.5 hrs longer than larger pipe. how Long does big pipe take to fill the tank??

Answer 1

Assume smaller pipe fills the tank in x hours and the larger one in (x-2.5) hours. Taking the given inf that both together can fill the tank in 8.4 hours, develop a quadratic equation in x, and solve it.

Larger pipe fills the tank in 15.65 hours whereas the smaller one takes 18.15 hours to fill it.

Answer 2

this is an algebra question, so you would probably get more answers in the math section than here in the engineering section

b= big pipe rate (tanks/hr)
s= small pipe rate (tanks/hr)

8.4 hrs *b tanks/hr +8.4*hrs * s tanks/hr = 1 tank
8.4b+8.4s=1

1/b hrs/tank = 1/s hrs/tank +2.5 hrs/tank
1=b/s + 2.5 b

so, from the first equation
s=(1-8.4b)/8.4

substituting
1=b/((1-8.4b/8.4))+2.5b

0=8.4b/(1-8.4b)+2.5b-1
0=(1-8.4b)*8.4b+(1-8.4b)*2.5b-1+8.4b

0=8.4b-8.4^2b^2+2.5b-(2.5)(8.4)b^2-1+8.4b
0=8.4b-70.6b^2+2.5b-21b^2-1+8.4b
0=-91.6 b^2+19.3b-1

I suspect I have made a mess of this. I don't have a pencil or paper where I am now and trying to type algebra isn't working too well. If I have done this right (which I sincerely doubt) then the quadratic formula will give a real positive root which will be, "b", the rate in tanks/hr for the big pipe. The reciprocal of which will be hours/tank.

If, as is likely, I didn't do the algebra right, perhaps you can get an idea from how I started.

good luck

Answer 3

You have 4 variables:
a. small pipe flowrate
b. large pipe flowrate
c. tank size
d. time to fill tank with big pipe only

However, you only have 3 equations:
1. 8.4 hrs x (a + b) = c
2. (d + 2.5 hrs) x a = c
3. d x b = c

Therefore, your question cannot be answered.

Answer 4

Assume larger pipe fills the tank in x hours and smaller pipe fills tank in x+2.50 hrs
so 1/x + 1/(x+2.50) = 1/ 8.404
By doing LCM
( (x+2.50)+x ) / ( x(x+2.50) ) = 1/8.404
By cross multiplication
8.404( x+ x+ 2.50) = x(x+2.50)
16.808x + 21.01 = x^2 + 2.50x
x^2 - 14.308x - 21.01
By using quadratic equation or engineering calculator
we get larger pipe x = 15.6 hours
smaller pipe x+2.50 = 15.6+2.50 = 18.1 hours

Answer 5

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