Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?
In a problem like this, we need to know what is the fraction of work each achieves in a unit time, say a minute.
If all three work together, add up the fraction of work they can do in one minute. The reciprocal is the time required in minutes.
Each minute, Jim can do 1/30th of the work, and Sue 1/45.
If the two of them work together, they can finish (1/30+1/45)=5/90=1/18 of the work in one minute. Therefore they would finish the work in 18 minutes.
Solve the same way when Tony chips in.
To find out how quickly all three can fill the pool together, we need to calculate the combined rate at which they fill the pool.
First, let's find the individual rates at which each person fills the pool:
Jim fills the pool in 30 minutes, so his rate is 1/30 pools per minute.
Sue fills the pool in 45 minutes, so her rate is 1/45 pools per minute.
Tony fills the pool in 1.5 hours, which is equal to 1.5 * 60 = 90 minutes. So his rate is 1/90 pools per minute.
Now, let's add up the rates of all three to get their combined rate of filling the pool:
Combined rate = Jim's rate + Sue's rate + Tony's rate
= 1/30 + 1/45 + 1/90 pools per minute
To add the rates, we need a common denominator, which is 90 in this case:
Combined rate = (3/90) + (2/90) + (1/90) pools per minute
= 6/90 pools per minute
Simplifying the combined rate, we get:
Combined rate = 1/15 pools per minute
Therefore, all three can fill the pool together at a rate of 1/15 pools per minute. To find out how quickly they can fill the pool together, we take the reciprocal of the combined rate:
Time taken to fill the pool = 1 / (1/15) minutes
= 15 minutes
So, all three can fill the pool together in 15 minutes.