Question 1175009
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Let *[tex \Large x] represent the number of hours Maria would take to clean the house alone.  Then*[tex \Large x\,+\,3] is the number of hours Jane would take to clean the house alone.


Maria can clean *[tex \Large \frac{1}{x}] of the house in one hour.  Jane can clean *[tex \Large \frac{1}{x\,+\,3}] of the house in one hour.  Working together, they could clean *[tex \Large \frac{1}{x}\ +\ \frac{1}{x\,+\,3}] of the house in one hour.


Adding the fractions:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\,+\,3)\ +\ x}{x(x\,+\,3)}\ =\ \frac{2x\,+\,3}{x^2\,+\,3x}]


represents the fractional portion of the house that they could clean in one hour working together.  Taking the reciprocal:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2\,+\,3x}{2x\,+\,3}]


represents the amount of time that it would take both to clean the whole house, and we know that this is equal to 2 hours, hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2\,+\,3x}{2x\,+\,3}\ =\ 2]


Solve for *[tex \Large x] to find the amount of time it would take Maria to clean the house by herself, and then calculate *[tex \Large x\ +\ 3] to find the amount of time it would take Jane to clean the house by herself. Hint:  Multiply both sides of the equation by the denominator on the left, collect like terms, solve the resulting quadratic, and discard any answer less than zero.

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
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