Question 270835
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Let *[tex \Large x] represent the number of days it takes Andrew to paint the house.  Then *[tex \Large 6x] represents the number of days it would take Bailey to paint the same house.


That means that Andrew can paint *[tex \Large \frac{1}{x}] of a house in 1 day, and Bailey can paint *[tex \Large \frac{1}{6x}] of a house in 1 day.  Working together they can paint:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{1}{6x}]


of a house in 1 day.


Performing the sum:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{7}{6x}]


That means that working together they can paint the whole house in:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{6x}{7}]


But we are given that they took 7 days to do the whole job last year, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{6x}{7}\ =\ 7]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6x\ =\ 49]


Which happens to be the number of days it would take Bailey working alone.  And then:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{49}{6}\ =\ 8\frac{1}{6}]


is the number of days it would take Andrew.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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