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 rate for each is
jim 1pool/30min
Sue 1pool/45min
Tony 1 pool/90min
The combined rate is the sum of all.
Now, do the volume=rate*time
1pool=(1/30 +1/45 +1/90) time
solve for time.
lim at x approaches negative infinity (sin^2x+cos^2x)
wow that looks pretty hard i really don't know about that one! good luck!
To find out how quickly all three of them can fill the pool together, we need to calculate their combined work rates. The work rate represents the amount of work done per unit of time.
Let's find the work rate for each person:
Jim's work rate = 1 pool / 30 minutes = 1/30 pools per minute
Sue's work rate = 1 pool / 45 minutes = 1/45 pools per minute
Tony's work rate = 1 pool / 1.5 hours = 1/90 pools per minute
Now, let's calculate their combined work rate:
Combined work rate = Jim's work rate + Sue's work rate + Tony's work rate
Combined work rate = 1/30 + 1/45 + 1/90 pools per minute
To add these fractions, we need to find a common denominator, which is 90:
Combined work rate = (3/90) + (2/90) + (1/90) pools per minute
Combined work rate = 6/90 pools per minute
Simplifying the fraction:
Combined work rate = 1/15 pools per minute
Now, we can find out how quickly all three can fill the pool together by calculating the reciprocal of the combined work rate:
Time taken to fill the pool = 1 / (1/15)
Time taken to fill the pool = 15 minutes
Therefore, it will take all three of them working together 15 minutes to fill the pool.