if you do a job in 4 hours, and your friend can do the same job but in 6 hours, and if you both work together how long will it take to complete the job?
your rate = job/4
friend's rate = job/6
combined rate = job/4 + job/6 = 5job/6
Time = job/rate = job/(5job/12))
= 12/5 hours or 2 hours and 24 minutes.
To find out how long it will take for you and your friend to complete the job, you can use the concept of work rates. Your work rate is 1 job in 4 hours, which means you can complete 1/4 of the job in one hour. Similarly, your friend's work rate is 1 job in 6 hours, or 1/6 of the job in one hour.
When you work together, you can add your work rates to find the combined work rate. So, your combined work rate is (1/4 + 1/6) jobs per hour.
To determine how long it will take both of you to complete the job, you need to find the reciprocal of the combined work rate. In other words, you divide 1 by the combined work rate.
So, the equation becomes:
1 / (1/4 + 1/6) = (1 / (3/12 + 2/12)) = 1 / (5/12) = 12/5 = 2.4
Therefore, when you and your friend work together, it will take approximately 2.4 hours to complete the job.