Jim can fill a pool in 30 min, sue can do it in 45 min, Tony can do it in 90min, how long would it take all three to fill the pool together? How would i figure this out?
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Jim's rate = pool/30
Sue's rate = pool/45
Tony'rate = pool/90
combined rate = pool/30 + pool/45 + pool/90
= (3pool + 2pool + pool)/90 = 6pool/90
= 2pool/30
time to fill pool with combined rate
= pool/(2pool/30)
= 1/(2/30)
= 15
Im still not sure how you are geting the (3pool+2pool+pool) where are those numbers coming from?
Jim can fill 3 pools in 90 minutes; Sue fills 2 pools in 90 minutes . . .
oh wow thank you so much i totally understand now
You're very welcome.
To figure out how long it would take all three of them to fill the pool together, you need to calculate their combined rate of work.
Let's first calculate the rates of work for each person:
- Jim's rate = 1 pool / 30 min = 1/30 pools per minute
- Sue's rate = 1 pool / 45 min = 1/45 pools per minute
- Tony's rate = 1 pool / 90 min = 1/90 pools per minute
To find the combined rate, add up their individual rates:
Combined rate = Jim's rate + Sue's rate + Tony's rate
Combined rate = 1/30 + 1/45 + 1/90 pools per minute
Now, we need to determine how long it would take to fill the pool with the combined rate. Since the rate is in pools per minute, the time to fill the pool will also be in minutes.
Time to fill the pool = 1 pool / Combined rate
Time to fill the pool = 1 / (1/30 + 1/45 + 1/90)
Now, let's simplify this equation:
Inverse of a sum = 1 / (1/a + 1/b + 1/c) = (ab + ac + bc) / (a * b * c)
Time to fill the pool = (30 * 45 * 90) / (45 * 90 + 30 * 90 + 30 * 45)
Now, let's calculate it:
Time to fill the pool = 1,350 / (4,050 + 2,700 + 1,350)
Time to fill the pool = 1,350 / 8,100
Time to fill the pool ≈ 0.1667 minutes
So, it would take approximately 0.1667 minutes for all three of them to fill the pool together.