Mike can assemble a computer table in 40 minutes and I can do it in 60 minutes.
If Mike works for 20 minutes before I join him, how long will it take us to finish?
He is half done.
task= time*rate
time= task/rate= 1/2 / (1/40+1/60)
time= 1/2 * 120/(3+2)=60/5=12min
To find out how long it will take for you and Mike to finish assembling the table together, we need to calculate how much work is done in 20 minutes by Mike and how much work is done in x minutes by both of you together.
Mike can assemble the computer table in 40 minutes, so in 20 minutes, he would have completed:
Work done by Mike in 20 minutes = (20 minutes / 40 minutes) * 1 computer table = 1/2 computer table
You can assemble the computer table in 60 minutes, so in x minutes, you would have completed:
Work done by you in x minutes = (x minutes / 60 minutes) * 1 computer table
Since you and Mike are working together, the total work done by both of you in x minutes would be:
Total work done by both of you in x minutes = (x minutes / 60 minutes) * 1 computer table + 1/2 computer table
Since you want to know how long it will take for both of you to finish, we set the total work done by both of you equal to 1 computer table:
(x minutes / 60 minutes) * 1 computer table + 1/2 computer table = 1 computer table
Now, we solve this equation for x to find the time it will take for both of you to finish:
(x / 60) + (1/2) = 1
Multiply both sides by 60:
x + 30 = 60
Subtract 30 from both sides:
x = 30
Therefore, it will take both of you 30 minutes to finish assembling the computer table together.