math
posted by muffy .
Shelby can paint a room in 4 hours. Zoe can paint the same room in 7 hours. How long will it take them to paint the room if they work together? If they start 9:30a.m., and want to see a movie that is playing 45 minutes from their house and starting 12:00 p.m., will they make it on time? If they can make it, how early are they? If they will be late, how late will they be?
Please let me know if I am correct.
First I took the average of 4 and 7 and got 5.5 hours. So they can both paint the room in 5.5 hours.
Next, If they start at 9:30 they will finish at 3:00
Next if they have to leave 45 minutes early to get to a 12:00 show, they should leave at 11:15.
Next, therefore, they will be 3:45 minutes late for the 12:00 show.

You cant trust the average always.
I assume you are using a rate equation,
amount=rate*time
Consider in 28 hours, shelby can paint 7, and Zoe can paint 4. So the combined rate = (7+4 rooms)/28 hrs= 11/28 rooms/hr
Now the time to paint one room
amount= rate*time
time= amount/rate= 1room/(11/28 room/hr)
time= 1*28/11 hrs= 2.54hrs= 2hrs 33min
If they start at 9:30, then they finish about three min after noon. Check my thinking and calculations.
Now on your thinking... Using the average 5.5hrs per room, but BOTH are working, that is the average for each, so time for both together would be 5.5/2= 2.75hrs, which is not 28/11 hrs (2.545hrs). SO don't use the average, throw away that thinking, it wont work. 
Thank you soooooooo much, you are a great teacher! I truly understand!