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July 12th, 2013, 08:28 AM   #1
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Rational Expression word problem. Please Help

This question doesn't have an answer at the back of the book and I'm unable to solve it.

Chris can clean a house in 3 hours and Cheryl can clean the house in 2 hours. Their son,
Tyler, can scatter toys all over the house in 4 hours. If Tyler starts scattering toys at the
same time Chris and Cheryl start cleaning, when (if ever) will the house be clean?
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July 12th, 2013, 09:16 AM   #2
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Re: Rational Expression word problem. Please Help

Since the least common multiple of 3, 2, and 4 is 12, I would look at how many houses the 3 of them will together clean in 12 hours. This is:

4 + 6 - 3 = 7

So, their house will be clean in 12/7 hr.
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July 12th, 2013, 11:46 AM   #3
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Re: Rational Expression word problem. Please Help

Hello, AKofTroy!

Quote:
Chris can clean a house in 3 hours and Cheryl can clean the house in 2 hours.
Their son, Tyler, can scatter toys all over the house in 4 hours.
If Tyler starts scattering toys at the same time Chris and Cheryl start cleaning,
when (if ever) will the house be clean?

















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July 13th, 2013, 11:35 AM   #4
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Re: Rational Expression word problem. Please Help

Thanks alot soroban. Word problems are the hardest in algebra. MarkFL, you could have put in more explanation.
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July 13th, 2013, 12:00 PM   #5
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Re: Rational Expression word problem. Please Help

Quote:
Originally Posted by AKofTroy
...MarkFL, you could have put in more explanation.
What more needed to be explained? Together, the 3 people's efforts results in 7 houses being cleaned in 12 hours...that's 12/7 hr/house.
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July 13th, 2013, 02:45 PM   #6
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Re: Rational Expression word problem. Please Help

I hadn't understood why you used LCM and where 4+6-3 came from.
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July 13th, 2013, 05:19 PM   #7
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Re: Rational Expression word problem. Please Help

Quote:
Originally Posted by AKofTroy
I hadn't understood why you used LCM and where 4+6-3 came from.
My apologies...I used LCM(2,3,4)= 12 since it is the smallest number into which 2,3, and 4 can all go into evenly. This alleviates the need to use fractions. The way [color=#00BF00]soroban[/color] worked the problem is the way I was taught in school, but another member here demonstrated the technique I showed above and I found it much simpler to use.
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