SOLUTION: Hi, I would like to say thank you for your help in advanced! Here is my question: A tank can be filled by a certain pipe in 18.0 hours. Five hours after this pipe is opene

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Hi, I would like to say thank you for your help in advanced! Here is my question: A tank can be filled by a certain pipe in 18.0 hours. Five hours after this pipe is opene      Log On


   

Question 993391: Hi,
I would like to say thank you for your help in advanced!
Here is my question:
A tank can be filled by a certain pipe in 18.0 hours. Five hours after this pipe is opened,it is supplemented by a smaller pipe which by itself could fill the tank in 24.0 hours. Find the total time, measured from the opening of the larger pipe, to fill the tank.

PLEASE PLEASE PLEASE explain your solution. I am lost with these kind of problems.
Thank you,
Anthony

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Thank you for asking.

The first pipe fills 1%2F18 of the tank volume in one hour (in each hour).

After  5  hour of working,  this pipe will fill  5%2F18  of the tank volume,  and  13%2F18  of the volume will remain still non-filled.

The second pipe fills  1%2F24  of the tank volume per hour.  When both pipes are at work,  they fill  1%2F18 + 1%2F24 = 4%2F72 + 3%2F72 = 7%2F72  of the tank volume for each hour.
They will fill the remaining volume of the tank in  13%2F18 : 7%2F72  hours.  Now,

13%2F18 : 7%2F72 = %2813%2A72%29%2F%2818%2A7%29 = %2813%2A4%29%2F7 = 52%2F7 = 73%2F7  hours.

Hence,  the total time,  measured from the opening of the larger pipe,  to fill the tank is  5 + 73%2F7 = 123%2F7  hour.


Many of typical  "joint work"  problems are considered and solved in the lesson  Using fractions to solve word problems on joint work  in this site.

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