A mechanic can do a job in 2hr. It takes his assistant 3hr to do the same job how long would it take them to complet the job if they worked together?
mechanic' rate --- 1/2
assistant's rate --- 1/3
combined rate = 1/2 + 1/3 = 5/6
time at combined rate = 1/(5/6)
= 6/5 hrs
or 1 hour 20 minutes
oops, 1/5 hr = 12 minutes, not 20 minutes
so 1 hour, 12 minutes
To find out how long it would take for the mechanic and his assistant to complete the job together, you can use the concept of their combined rates of work.
First, determine each person's rate of work. The mechanic can complete the job in 2 hours, so his rate of work is 1 job per 2 hours (1 job/2 hours = 1/2 job per hour). The assistant can complete the same job in 3 hours, so his rate of work is 1 job per 3 hours (1 job/3 hours = 1/3 job per hour).
To find their combined rate of work, add their individual rates of work together: (1/2 job per hour) + (1/3 job per hour) = (3/6 job per hour) + (2/6 job per hour) = 5/6 job per hour.
This means that their combined rate of work is 5/6 job per hour.
Now, to determine how long it would take them to complete the job together, divide the total job (1 job) by their combined rate of work (5/6 job per hour):
(1 job) ÷ (5/6 job per hour) = (1 job) × (6/5 job per hour) = 6/5 hour.
Therefore, it would take them 6/5 hour, or 1.2 hours, to complete the job if they worked together.