SOLUTION: An oil tanker has 2 inlet pipes.Pipe #1 can fill the tank in 6 hours, pipe #2 can fill it in 2 hours. An outlet valve can empty the tank in 24 hours. How long will it take to fill

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An oil tanker has 2 inlet pipes.Pipe #1 can fill the tank in 6 hours, pipe #2 can fill it in 2 hours. An outlet valve can empty the tank in 24 hours. How long will it take to fill       Log On


   

Question 7910: An oil tanker has 2 inlet pipes.Pipe #1 can fill the tank in 6 hours, pipe #2 can fill it in 2 hours. An outlet valve can empty the tank in 24 hours. How long will it take to fill the tank if all 3 are fully opened?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's see what can happen in 1 hour:
If inlet #1 can fill in 6 hours, then it can fill 1/6 of the tank in 1 hour.
If inlet #2 can fill in 2 hours, then it can fill 1/2 of the tank in 1 hour.
If the outlet can empty it in 24 hours, then it can empty 1/24 (-1/24) of the tank in 1 hour. So, in 1 hour, altogether, we get:
1%2F6+%2B+1%2F2+-+1%2F24+=+4%2F24+%2B+12%2F24++-+1%2F24 = 15%2F24
So, in 1 hour, with all three valves fully opened, 15/24 of the tank can be filled. You could write this as: 15/24 of 1 tank = 1 hour.
Multiply both sides by the multiplicative inverse of (15/24) to find how long to fill the whole tank:
This means it will take 24/15 hours to fill the tank.
24%2F15+=+%281+%2B+9%2F15%29+hours = 1 hour and 36 minutes to fill the tank.