Question

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?

Answer 1

They could complete the job together in `12/11` days.

Explanation:

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 `1/4`, i.e. in one day Sam could complete `1/4`th of the job.

Lisa's rate is one job completed in 6 days, or `1/6`. She could complete `1/6`th of the job in one day.

Tom's rate is one job completed in 2 days, or `1/2`. He could complete `1/2` of the job in one day.

Together, they could complete `1/4 + 1/6 +1/2` of the job in one day.

We are trying to find the rate at which Sam, Lisa and Tom could complete the job together, or one job in `x` days, for a rate of `1/x`.

`1/4 + 1/6+1/2 =1/x`

The least common denominator is `12x`.

Multiplying through by the LCD gives:

`12x ( 1/4) +12x (1/6) + 12x ( 1/2) = 12x ( 1/x)`

`3x + 2x + 6x=12`

`11x=12`

`11x/11 =12/11`

`x = 12/11` days