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?
They could complete the job together in
Sam: 4 days
Lisa: 6 days
Tom: 2 days
This is a "rate" problem. The rate is jobs per day, or job/day.
Sam's rate is one job completed in 4 days, or
Lisa's rate is one job completed in 6 days, or
Tom's rate is one job completed in 2 days, or
Together, they could complete
We are trying to find the rate at which Sam, Lisa and Tom could complete the job together, or one job in
The least common denominator is
Multiplying through by the LCD gives: