SOLUTION: Working together, two pipes can fill the tank in 2 hours and 6 minutes. Working alone, the larger pipe fills the tank in 4 hours less time than the smaller on. How long does the la

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Working together, two pipes can fill the tank in 2 hours and 6 minutes. Working alone, the larger pipe fills the tank in 4 hours less time than the smaller on. How long does the la      Log On


   

Question 396577: Working together, two pipes can fill the tank in 2 hours and 6 minutes. Working alone, the larger pipe fills the tank in 4 hours less time than the smaller on. How long does the larger pipe take?
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Working together, two pipes can fill the tank in 2 hours and 6 minutes. Working alone, the larger pipe fills the tank in 4 hours less time than the smaller on. How long does the larger pipe take?
6 minutes=6/60 = 1/10 hours
both pipes 2 1/10 hours= 23/10 hours
they do 10/23 of the filling in 1 hour
.....
smaller pipe takes x hours
it does 1/x of filling in 1 hour
....
larger pipe takes x-4 hours
it does1/(x-4) of the job in 1 hour
...
1/x + 1/(x-4)= 10/23
LCD = x(x-4)
(x-4+x)/x(x-4)=10/23
cross ultiply
23(2x-4)=10x(x-4)
46x-92=10x^2-40x
10x^2-86x+92=0
/2
5x^2-43x+46=0
solve using quadratic formula
Find the roots of the equation by quadratic formula
a= 5 , b = -43 , c =46
b^2-4ac= 929 .
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%2843%2Bsqrt%28929%29%29%2F%2810%29
7.3 hours
...
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2= (43-sqrt(929))/(10)
x2=1.25 this is not possible since larger pipe takes four hours less.
So larger pipe takes 7.34-4 = 3.3 hours
m.ananth@hotmail.ca

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Working together, two pipes can fill the tank in 2 hours and 6 minutes. Working alone, the larger pipe fills the tank in 4 hours less time than the smaller on. How long does the larger pipe take?
Let 1/x = hourly work rate of smaller pipe
1/(x-4) = hourly work rate of larger pipe
2 hrs and 6 min = 2.1 hours
1/2.1 = hourly work rate when both pipes working
sum of the individual work rates = work rate when working together
1/x + 1/(x-4) = 1/(2.1)
LCD =x(x-4)(2.1)
(x-4)(2.1)+x(2.1)=x(x-4)
2.1x-8.4+2.1x=x^2-4x
x^2-8.2x+8.4=0
solve with the following quadratic equation with a=1, b=-8.2, c=8.4
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(-(-8.2)+ - sqrt((8.2)^2-4*1*8.4)/2
= (8.2 +-sqrt(67.24-33.6)/2
= (8.2 +-sqrt(33.64)/2
x=(8.2 +-5.8)/2
x=14/2 or 2.4/2
x=7 or x=1.2(reject because this would give a negative rate for the larger pipe.
ans: working alone the larger pipe would take 7-4 = 3 hours
working alone the smaller pipe would take 7 hours