Matt and Jena, working together, can clean the house in 9 hours. Working alone, Jena takes three times as long as Matt. How long does it take Matt to clean the house.
If Matt takes x hours, then Jena takes 3x
1/x + 1/3x = 1/9
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Matt=x
Jena=y
x+y=9
Jena takes three times as long as Matt
x=y(1/3)
3x=y
x+3x=9
4x=9
x=9/4
Matt=9/4 or 2.25 hours
To solve this problem, we can assign variables to represent the time it takes for Matt and Jena to clean the house alone. Let's say it takes Matt x hours and Jena 3x hours.
According to the given information, when they work together, they can clean the house in 9 hours. This means that the rate at which they work together is 1/9th of the house per hour.
Matt's rate of work is 1/x of the house per hour, and Jena's rate of work is 1/(3x) of the house per hour.
Since their rates of work add up when they work together, we can set up the equation:
1/x + 1/(3x) = 1/9
To solve the equation, we can find a common denominator:
(3 + 1)/(3x) = 1/9
Simplifying further:
4/(3x) = 1/9
Cross-multiplying:
4 * 9 = 3x
36 = 3x
Dividing both sides by 3:
x = 12
Therefore, it takes Matt 12 hours to clean the house alone.