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? ANYBODY KNOW THE ANSWER??
Jim's rate = Pool/30
Sue's rate = Pool/45
Tony's rate = Pool/90
combined rate = pool/30 + pool/45 + pool/90
= 6pool/90 = pool/15
So time working combined = pool/(pool/15) = 15
it will take 15 minutes.
To find out how quickly all three can fill the pool together, we need to calculate their combined rate of work.
First, let's find out how much of the pool Jim can fill in 1 minute. Since he can fill the pool in 30 minutes, his rate of work is 1/30 of the pool per minute.
Similarly, Sue can fill 1/45 of the pool per minute, and Tony can fill 1/90 of the pool per minute (since 1 ½ hours is equal to 90 minutes).
Now, to find their combined rate of work, we sum up their individual rates. Thus, the combined rate of work for Jim, Sue, and Tony is:
1/30 + 1/45 + 1/90.
To combine these fractions, we need to find a common denominator, which in this case is 90. Rewriting the fractions with this common denominator, we get:
3/90 + 2/90 + 1/90.
Combining the numerators, we have:
(3 + 2 + 1)/90 = 6/90.
Reducing this fraction, we get:
1/15 of the pool per minute.
Therefore, all three can fill the pool together at a rate of 1/15 of the pool per minute. To determine how quickly they can fill the pool completely, we need to take the reciprocal of this rate:
15/1 = 15 minutes.
Hence, all three can fill the pool together in 15 minutes.