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?

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Answer 1 · 2016-10-25T01:36:56

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

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