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?
Sam's rate = job/4
Lisa's rate = job/6
Tom's rate = job/2
time for all 3 working together
= job/(job/4 + job/6 + job/2)
= job/(11job/12)
= job * 12/(11job)
= 12/11
it would take them 1 1/11 days
thanks but the answer is 13 i just don't know how to get it.
The answer of 13 days would be totally illogical!
Gee, Tom working alone can do the job in 2 days, and then he even has help, so it would obviously take less than 2 days !!!!
To find out how long it would take for Sam, Lisa, and Tom to complete the job together, we need to calculate their combined work rate.
Let's start by calculating each person's work rate per day. We can determine this by taking the reciprocal of the time it takes for each person to complete the job individually:
Sam's work rate per day = 1 job / 4 days = 1/4 job per day
Lisa's work rate per day= 1 job / 6 days = 1/6 job per day
Tom's work rate per day = 1 job / 2 days = 1/2 job per day
Now, to find their combined work rate, we add up their individual work rates:
Combined work rate = Sam's work rate + Lisa's work rate + Tom's work rate
= 1/4 + 1/6 + 1/2
To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 4, 6, and 2 is 12. So we need to rewrite the fractions with the denominator of 12:
Combined work rate = 3/12 + 2/12 + 6/12
= 11/12 job per day
Therefore, Sam, Lisa, and Tom together can complete 11/12 of a job per day.
To find out how long it would take for them to complete the entire job, we can calculate the reciprocal of their combined work rate:
Time taken to complete the job = 1 job / Combined work rate
= 1 / (11/12)
= 12/11 days
So, it would take Sam, Lisa, and Tom approximately 12/11 days, which is about 1.09 days, to complete the job if they work together.