AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Expert: Abe Mantell Date: 7/6/2008 Subject: Word Problem
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.
