Question 265496: I am doing a practice exam for my GRE and I am stumped on this type of problem. Can you help?
3. 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
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = units
this translates to:
number of units produced per minute * number of minutes = number of units produced.
the number of units produced is 1 full pool.
jim can fill the pool in 30 minutes which means jim can fill 1/30 of the pool each minute.
1/30 * 30 = 1
sue can fill the pool in 45 minutes which means sue can fill 1/45 of the pool each minute.
1/45 * 45 = 1
tony can fill the pool in 1 and 1/2 hours which means that tony can fill the pool in 90 minutes which means that tony can fill 1/90 of the pool each minute.
1/90 * 90 = 1
when they work together, their combined rates are additive.
if we let x = the number of minutes it takes to fill the pool, then we have:
rate * x = 1
the combined rate is equal to jim's rate plus sue's rate plus tony's rate.
formula becomes:
(1/30 + 1/45 + 1/90) * x = 1
1/30 + 1/45 + 1/90 = 3/90 + 2/90 + 1/90 = 6/90 = 1/15.
their combined rate is 1/15 of the pool every minute.
formula becomes:
1/15 * x = 1
multiply both sides of this equation by 15 to get:
x = 15
working together, they will take 15 minutes to fill the pool.
in 15 minutes jim has filled 1/30 * 15 = 15/30 = 1/2 of the pool.
in the same 15 minutes, sue has filled 1/45 * 15 = 1/3 of the pool.
in the same 15 minutes, tony has filled 1/90 * 15 = 1/6 of the pool.
1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1 full pool.
your answer is selection B (15 minutes).
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