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 they worked together to complete it?
combined rate = 1/4 + 1/6 + 1/2 = 11/12
so time taken for working at combined rate = 1/(11/12)
= 12/11 hours
or 1 hour and about 5 minutes
To determine how long it would take for Sam, Lisa, and Tom to complete the job together, we can calculate their combined work rate.
We start by finding each person's work rate, which is determined by how much of the job they can complete in one day:
- Sam can complete the job in 4 days, so his work rate is 1 job / 4 days = 1/4 job per day.
- Lisa can complete the job in 6 days, so her work rate is 1 job / 6 days = 1/6 job per day.
- Tom can complete the job in 2 days, so his work rate is 1 job / 2 days = 1/2 job per day.
To find their combined work rate when working together, we add their individual work rates:
1/4 + 1/6 + 1/2 = (3/12) + (2/12) + (6/12) = 11/12 job per day.
This means that the three of them can complete 11/12 of the job in one day when they work together.
To find how long it would take to complete the entire job, we divide the total job by their combined work rate:
1 job / (11/12 job per day) = (1 * 12) / 11 = 12/11 days.
Therefore, it would take Sam, Lisa, and Tom approximately 12/11 days, or about 1.09 days, to complete the job together.