Expert: Abe Mantell - 7/6/2008

Question
I am stuck on finding a formula to solve the following word problem: If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? Can you help me to figure out the right formula for this problem?

Answer
Since work = rate x time...

The rate Sam can work is 1/4 (of a job/day), Lisa works at
the rate of 1/6 (of a job/day), and Tom works at the rate of
1/2 (job/per day)...thus, together, they work at the rate
1/4 + 1/6 + 1/2 = 11/12. Thus, if "t" is the time it takes them
all to complete the job, then (11/12)t=1 ==> t=12/11 day, or
about 1 day, 2 hrs, 10 min, 55 sec.

Abe