SOLUTION: one pipe can be used to fill a tank in 48 minutes and another can be used to fill it in one hour and 12 minutes. How will it take to fill the tank if both pipes are used?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: one pipe can be used to fill a tank in 48 minutes and another can be used to fill it in one hour and 12 minutes. How will it take to fill the tank if both pipes are used?       Log On


   

Question 692382: one pipe can be used to fill a tank in 48 minutes and another can be used to fill it in one hour and 12 minutes. How will it take to fill the tank if both pipes are used?
Found 2 solutions by Edwin McCravy, partha_ban:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

one pipe can be used to fill a tank in 48 minutes and another can be used to fill it in one hour and 12 minutes. How will it take to fill the tank if both pipes are used? 
We are given the first pipe's filling rate as 1 pool per 48 minutes, or
%281_POOL%29%2F%2848_MIN%29 or 1%2F48 or 1%2F80POOL%2FMIN%29


We let X = the number of minutess it will take both machines working together to
process the data.

So we can say that their combined filling rate is 1 pool per
X hours, or %281_POOL%29%2F%28X_HOURS%29 or 1%2FXPOOL%2FHR%29.

The equation comes from:

      %28matrix%284%2C1%2C%0D%0A%0D%0AFirst%2C+%22pipe%27s%22%2Cfilling%2C+rate%29%29%22%22%2B%22%22%28matrix%284%2C1%2C%0D%0A%0D%0AFirst%2C+%22pipe%27s%22%2C+filling%2C+rate%29%29%22%22=%22%22%28matrix%284%2C1%2C%0D%0A%0D%0ATheir%2C+combined%2C+filling%2C+rate%29%29.

              1%2F48%22%22%2B%22%221%2F80%22%22=%22%221%2FX

Solve that by getting an LCD of 240X

Edwin

Answer by partha_ban(41) About Me  (Show Source):
You can put this solution on YOUR website!
First pipe fills the tank in 48 mins
So in 1 minute, it will fill 1/48 part of the tank.
Second pipe fills the tank in 1 hr 12 mins or in 72 mins
So in 1 minute, 2nd pipe will fill 1/72 parts of the tank.
When both the pipes fill the tank, in 1 minute, they will fill
1%2F18+%2B+1%2F72 parts of the tank
= %283+%2B+2%29%2F144
= 5%2F144 parts
Therefore, the tank will be full in 1 / (5/144) minutes
= 144/5 mins
= 22 mins 48 secs when both the pipes fill it