SOLUTION: Word Problem: If John cleans a house in 8 hours and Julie cleans a similar house in 6 hours, how long should it take them to clean another similar house working together?

Question 98216: Word Problem:
If John cleans a house in 8 hours and Julie cleans a similar house in 6 hours, how long should it take them to clean another similar house working together?
Found 2 solutions by checkley71, ptaylor:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
8*6/(8+6)=48/14=3.43 HOURS TO DO THE JOB TOGETHER.

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes John and Julie to clean the house working together
John cleans at the rate of 1/8 house per hour
Julie cleans at the rate of 1/6 house per hour
Together, they clean at the rate of (1/8+1/6) house per hour, or
1/8+1/6 =3/24+4/24= 7/24 house per hour
Now our equation to solve is:
(7/24)x=24/24 (note: here 24/24 represents 1 house)
7x=24 divide both sides by 7
x=24/7 or 3 3/7 hours

Hope this helps----ptaylor
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