SOLUTION: Latoya can paint five 10-foot-by-14-foot rooms by herself in 14 hours. Lisa can paint five 10-foot-by-14-foot rooms by herself in 10 hours. Working together, how long would it take

Question 1076779: Latoya can paint five 10-foot-by-14-foot rooms by herself in 14 hours. Lisa can paint five 10-foot-by-14-foot rooms by herself in 10 hours. Working together, how long would it take to paint 5 10-foot-by-14 foot rooms?
(Please show the work! I really want to understand this problem.)
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
The tasks in the question are alike. How long does it take to paint 5 10x14 rooms. Latoya can do it in 14 hours, or 1/14th of the task in an hour. Similarly, Lisa can finish 1/10th of the task per hour. Let n be the time it takes them working together. Then:
1/14 + 1/10=1/n
5n+7n=70
12n=70
n=70/12=35/6
Working together, it takes them 35/6 hours, or 5 hours and 50 minutes. ☺☺☺☺
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