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

Question

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

phi · Answer

this is similar to rate*time = distance,  except you now use
rate * time =  1 job  (1 filled pool in this case)

Jim's rate is 1 job/30 min
Sue's  rate    1 job/45 min
Tony's  rate  1 job/90 min

if they all work together for the same length of time, they fill the pool:
 jim's rate  *  T    +   Sue's rate *T  + Tony's rate * T = 1 job
factor out the T,  add up the rates, and solve for T