SOLUTION: It takes one day to fill the vat with this large pipe; two days with that' The third pipe needs but one day more; The fourth pipe fills the vat in four. If all four pipes together

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes one day to fill the vat with this large pipe; two days with that' The third pipe needs but one day more; The fourth pipe fills the vat in four. If all four pipes together       Log On


   

Question 426337: It takes one day to fill the vat with this large pipe; two days with that' The third pipe needs but one day more; The fourth pipe fills the vat in four. If all four pipes together fun, How many HOURS before the task is done?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It takes one day to fill the vat with this large pipe; two days with that'
The third pipe needs but one day more; The fourth pipe fills the vat in four.
If all four pipes together run, How many HOURS before the task is done?
:
Let's use hrs for this, since it wants the solution in hours
:
Let t = time required by all 4 pipes working together
Let the completed job = 1; (a full vat)
:
t%2F24 + t%2F48 + t%2F72 + t%2F96 = 1
The common denominator is 288, multiply thru by that, results:
12t + 6t + 4t + 3t = 288
25t = 288
t = 288%2F25
t = 11.52 hrs for all four to complete the task
:
:
:
Let's check that to be sure
11.52%2F24 + 11.52%2F48 + 11.52%2F72 + 11.52%2F96 =
.48 + .24 + .16 + .12 = 1; confirms our solution of 11.52 hrs