SOLUTION: Kim can paint the garage door in 2 hours and Jim can paint the same door in 1 hour. How long will it take them if they work together?

Question 1078031: Kim can paint the garage door in 2 hours and Jim can paint the same door in 1 hour. How long will it take them if they work together?
Found 3 solutions by josmiceli, amfagge92, Edwin McCravy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Kim's rate of working:
[ 1 garage door ] / [ 2 hrs ]
Jim's rate of working:
[ 1 garage door ] / [ 1 hr ]
Let = their time in hrs to paint the door
if they work together
Their rate working together:
[ 1 garage door ] / [ t hrs ]
-----------------------------
Add their rates of working to get their
rate working together

Multiply both sides by

hrs
-------------------
Convert this result to minutes

It will take them 40 minutes to paint the
door if they work together

Answer by amfagge92(93)   (Show Source): You can put this solution on YOUR website!
1.5hrs

Answer by Edwin McCravy(20063)   (Show Source): You can put this solution on YOUR website!
Notice that the preceding answer 1.5 hrs, could not be correct because
Jim alone could paint the door in 1 hour. Surely Kim couldn't slow
Jim down that much. LOL

Kim can paint the garage door in 2 hours and Jim can paint the same door in 1 hour. How long will it take them if they work together?

You can do it with or without algebra. Without algebra, just basic math: If both work together for 2 hours painting garage doors (say in a new development of houses), Kim will paint 1 garage door while Jim, the faster will paint 2 garage doors, so together they can paint 3 garage doors in 2 hours. So they can paint 1 garage door in 1/3 of 2 hours which is 1/3 of 120 minutes or 40 minutes. With algebra:

How long will it take them if they work together?

Let the answer be x hours.

Kim can paint the garage door in 2 hours.

So Kim's painting rate is 1 door per 2 hours or or

Jim can paint the same door in 1 hour

So Kim's painting rate is 1 door per 1 hour or or Together they can paint the same door in x hours: So together their combined painting rate is 1 door per x hours or or The equation comes from: Multiply through by 2x 2/3 of an hour is 2/3 of 60 minutes = 40 minutes. Edwin

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