time and work

Question

a and b can do a work in 18 days b and c can do it in 24 days a and c do it in 36 days. in how many days will a b and c finish it working together and separately?

Answer 1

Use a, b and c to mean the time for each to complete the jobs solo.

In one day each can do 1/a, 1/b and 1/c of the job. 1/a+1/b=1/18 means a and b can complete 1/18 of the job working together. Similarly, 1/b+1/c=1/24 and 1/a+1/c=1/36. Add these three equations together: 2/a+2/b+2/c=1/18+1/24+1/36=4/72+3/72+2/72=9/72=1/8; 1/a+1/b+1/c=1/16 so working together they can do the job in 16 days. 1/c=1/16-1/18 (because 1/a+1/b=1/18) = 9/144-8/144=1/144, so c=144; 1/a=1/16-1/24=3/48-2/48=1/48, so a=48; 1/b=1/16-1/36=5/144, so b=144/5=28.8=28 days 19 hrs 12 mins.

CHECKS

1/48+5/144=3/144+5/144=8/144=1/18. So a and b complete the job in 18 days.

5/144+1/144=6/144=1/24. b and c complete in 24 days.

1/48+1/144=3/144+1/144=4/144=1/36. a and c complete in 36 days.