Thomas in 4 hours. Julia can do the same job in 6 hours. How many hours will it take the two of them to do the job if they work together?
Assuming there is no change in productivity..
In one hour, Thomas does 1/4=25% of the job, while Julia does 1/6=16.66%. Combined they would do 25%+16.66% = 41.66% of the job in 1 hour. So, 1/.4166= 2.4 hours
To find out how many hours it will take Thomas and Julia to complete the job together, we need to determine their combined work rate.
Let's start by calculating their individual work rates:
Thomas can complete the job in 4 hours, so his work rate is 1 job / 4 hours = 1/4 job per hour.
Julia can complete the job in 6 hours, so her work rate is 1 job / 6 hours = 1/6 job per hour.
To find their combined work rate, we add their individual work rates together:
Combined work rate = Thomas's work rate + Julia's work rate
= 1/4 job per hour + 1/6 job per hour
= (6 + 4) / (4 * 6) job per hour
= 10 / 24 job per hour
= 5 / 12 job per hour.
Now, to find how many hours it will take them to complete the job together, we divide the total job by their combined work rate:
Time = Total job / Combined work rate
= 1 job / (5 / 12 job per hour)
= 1 * (12 / 5) hours / 1
= 12 / 5 hours.
Therefore, it will take Thomas and Julia 12/5 hours, or 2.4 hours, to complete the job when they work together.