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 1.5 hours. How quickly can all three fill the pool together?
A.12 minutes
B.15 minutes
C.21 minutes
D.23 minutes
E.28 minutes
I got 53 minutes, but there was no answer.
In 1.5 hours,
Tony can do one pool
Sue can do 2 pools
Jim can do 3 pools
pools=rate*time
combined rate=6pools/1.5 hrs=4pools/hr
time=pools/rate= 1pool/(4pools/hr)=1/4 hr= 15 min
To find out how quickly all three can fill the pool together, we can use the concept of work rates. Let's assume that the total capacity of the pool is 1 (the unit doesn't matter here).
First, let's find the work rate of each person. Work rate is defined as the amount of work done per unit of time.
Jim can fill the pool in 30 minutes, so his work rate is 1 pool / 30 minutes = 1/30 pool per minute.
Sue can fill the pool in 45 minutes, so her work rate is 1 pool / 45 minutes = 1/45 pool per minute.
Tony can fill the pool in 1.5 hours, which is equal to 90 minutes. Therefore, his work rate is 1 pool / 90 minutes = 1/90 pool per minute.
Now, let's add up their work rates to find the combined work rate when they work together.
Combined work rate = Jim's work rate + Sue's work rate + Tony's work rate
Combined work rate = 1/30 + 1/45 + 1/90
To add fractions, you need a common denominator. In this case, it is 90.
Combined work rate = (3/90) + (2/90) + (1/90) = 6/90 = 1/15 pool per minute.
Therefore, all three together can fill the pool at a rate of 1/15 pool per minute. To find how quickly they can fill the pool together, we take the reciprocal of their combined work rate:
Time = 1 / Combined work rate = 1 / (1/15) = 15 minutes.
So, the correct answer is option B. All three can fill the pool together in 15 minutes.