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?
A. 12 minutes
B. 15 minutes
C. 21 minutes
D. 23 minutes
E. 28 minutes
Jim 1/30 pools per minute
Sue 1/45 pools/min
Tony 1/90 pools/ min
Total = 3/90 + 2/90 + 1/90 = 6/90 = 1/15 pools/min
(1/15) pools /min * t = 1 pool
t = 15 min
Tony fills 1/6 in a quarter hour, not 1/4
1/2 + 1/3 +1/6 = 1 pool
To determine how quickly all three can fill the pool together, we need to find the rate at which each person fills the pool.
Let's start by finding Jim's rate. Jim can fill the pool in 30 minutes, so his rate is 1/30 (1 pool per 30 minutes).
Next, let's find Sue's rate. Sue can fill the pool in 45 minutes, so her rate is 1/45 (1 pool per 45 minutes).
Finally, let's find Tony's rate. Tony can fill the pool in 1 ½ hours, which is equal to 90 minutes. So his rate is 1/90 (1 pool per 90 minutes).
To find the combined rate of all three, we simply add their individual rates together:
Combined rate = Jim's rate + Sue's rate + Tony's rate
Combined rate = 1/30 + 1/45 + 1/90
Now, let's simplify this equation by finding a common denominator:
Combined rate = (3/90) + (2/90) + (1/90)
Combined rate = 6/90
Therefore, the combined rate of all three is 6/90 (6 pools per 90 minutes).
To find the time it takes for all three to fill the pool together, we can use the formula: time = 1/rate
time = 1 / (6/90)
time = 90/6
time = 15 minutes
Therefore, all three can fill the pool together in 15 minutes.
So, the answer is B. 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 determine the rate at which each person fills the pool individually.
Jim fill the pool in 30 minutes, so his rate of work is 1 pool per 30 minutes, or 1/30 pools per minute.
Sue fill the pool in 45 minutes, so her rate of work is 1 pool per 45 minutes, or 1/45 pools per minute.
Tony fill the pool in 1 ½ hours, which is equivalent to 1.5 hours or 90 minutes. So his rate of work is 1 pool per 90 minutes, or 1/90 pools per minute.
To calculate their combined rate of work, we add up their individual rates of work:
1/30 + 1/45 + 1/90 = 3/90 + 2/90 + 1/90 = 6/90 = 1/15
So, together, they can fill 1 pool in 15 minutes.
Therefore, the answer is B. 15 minutes.