SOLUTION: Pipe A can fill a tank in 4 hrs. If pipe B works alone, it takes 3 hrs longer to fill the tank than if both pipes work together. How long will it take for pipe B to fill the tank i

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pipe A can fill a tank in 4 hrs. If pipe B works alone, it takes 3 hrs longer to fill the tank than if both pipes work together. How long will it take for pipe B to fill the tank i      Log On


   

Question 318747: Pipe A can fill a tank in 4 hrs. If pipe B works alone, it takes 3 hrs longer to fill the tank than if both pipes work together. How long will it take for pipe B to fill the tank if it works alone?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Output
Ra%2A4=Z where Z is the tank volume.
Ra=Z%2F4%0D%0A%7B%7B%7B%28Ra%2BRb%29%2At=Rb%28t%2B3%29=Z
Ra%2BRb=Z%2Ft
Z%2F4%2BRb=Z%2Ft
1.Rb=Z%2Ft-Z%2F4
.
.
.
2.Rb=Z%2F%28t%2B3%29
Substitute into eq. 2,
Z%2Ft-Z%2F4=Z%2F%28t%2B3%29
1%2Ft-1%2F4=1%2F%28t%2B3%29
Multiply both sides by 4t%28t%2B3%29
4%28t%2B3%29-t%28t%2B3%29=4t
4t%2B12-t%5E2-3t=4t
-t%5E2-3t%2B12=0
t%5E2%2B3t-12=0
Use the quadratic equation,
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+
t+=+%28-3+%2B-+sqrt%28+9%2B48+%29%29%2F%282%29+
t+=+%28-3+%2B-+sqrt%28+57%29%29%2F%282%29+
Only the positive result makes sense here.
t+=+%28-3+%2Bsqrt%2857%29%29%2F2+
It takes Pipe B t%2B3 to fill the tank,
t%2B3=+%28-3%2B6+%2Bsqrt%2857%29%29%2F2+
highlight%28t%2B3=+%283+%2Bsqrt%2857%29%29%2F2%29+ or approximately,
t%2B3=+5.27 hours