Jim can fill a pool carrying bucks 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?
The answer is 15 minutes. But how?
Figure the rate each can fill the pool
jim rate= 1/30 (1pool/30 min)
same relation for others.
The total rate then is the sum...
ratetotal=1/30 + 1/45 + 1/90
so we have one pool to do in this rate in some time T.
1= ratetotal*time
solve for time.
BobP answered this correctly, I thought I'd just answer it for the practice.
This kind of problem requires you to determine the individual rates, then add them to get a total answer. It looks like
1pool(1/30min + 1/45min + 1/90min) = 1pool (6/90min) = 1pool/15min
These kinds of problems are very common on tests for some reason. Change the numbers and try working another problem similar to this just for practice.
1/T = 1/t1 + 1/t2 + 1/t3.
1/T = 1/30 + 1/45 + 1/90,
1/T = 3/90 + 2/90 + 1/90 = 6/90,
T = 90/6 = 15 Min.
To find out how quickly all three, Jim, Sue, and Tony, can fill the pool together, we need to determine the total rate at which they can fill the pool.
Let's start by figuring out the rate at which each person fills the pool:
Jim's rate: Jim can fill the pool in 30 minutes. So his rate is 1 pool per 30 minutes, or 1/30 pool per minute.
Sue's rate: Sue can fill the pool in 45 minutes. So her rate is 1 pool per 45 minutes, or 1/45 pool per minute.
Tony's rate: Tony can fill the pool in 1 ½ hours, which is equivalent to 90 minutes. So his rate is 1 pool per 90 minutes, or 1/90 pool per minute.
Now, let's calculate the total rate at which they can fill the pool by adding up their individual rates:
Total Rate = Jim's rate + Sue's rate + Tony's rate
Total Rate = 1/30 pool per minute + 1/45 pool per minute + 1/90 pool per minute
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 90:
Total Rate = (3/90 + 2/90 + 1/90) pool per minute
Total Rate = 6/90 pool per minute
Now, we have the total rate at which they can fill the pool. To find out how quickly they can fill the pool together, we need to find the time it takes to fill 1 pool at this rate:
1 pool = Total Rate * Time
Since the total rate is 6/90 pool per minute, we can set up the equation:
1 = (6/90) * Time
To solve for Time, we can multiply both sides of the equation by 90/6:
Time = (90/6) / (6/90)
Time = 15 minutes
Therefore, all three of them can fill the pool together in 15 minutes.