Question 633238
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Let *[tex \LARGE x] represent the time taken by the more efficient worker (#1), then *[tex \LARGE x\ +\ 4] is the time taken by the other guy (#2).


#1 can do the whole job in *[tex \LARGE x] hours, so he can do *[tex \LARGE \frac{1}{x}] of the job in one hour.  Likewise #2 can do *[tex \LARGE \frac{1}{x\ +\ 4}] of the job in one hour.  Working together, they can do


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{1}{x\ +\ 4}]


of the job in 1 hour, but we are given that they can do the whole job together in 9 hours, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{1}{x\ +\ 4}\ =\ \frac{1}{9}]


Apply the LCD (the product of the two denominators in the LHS) to add the two rational expressions in the left.  Then cross-multiply and collect terms.  Solve the resulting quadratic in *[tex \LARGE x] to get #1's time and calculate *[tex \LARGE x\ +\ 4] to get #2's time.


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