Question 511128
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Let *[tex \Large x] represent the number of minutes it would take the apprentice working alone to complete the part of the task that Tina and the apprentice worked on together.  Then *[tex \Large \frac{3x}{4}] is the number of minutes Tina would have taken on that part of the task if working alone.  Then the apprentice could do *[tex \Large \frac{1}{x}] of that part of the job in one minute, and Tina could do *[tex \Large \frac{4}{3x}] of that part of the job in one minute.  Since 2 hours and 16 minutes is 2 times 60 plus 16 equals 136 minutes, working together they performed *[tex \Large \frac{1}{136}] of the job in one minute.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ +\ \frac{4}{3x}\ =\ \frac{1}{136}] 


You can check the arithmetic for yourself, but it comes out to *[tex \Large x\ =\ 317\frac{1}{3}] minutes.


That is the amount of time, working alone, it would take the apprentice to do the part where they worked together.


The amount of time Tina would take for that same part of the job would simply be 3/4 of that time, or *[tex \Large \frac{3}{4}\ \times\ 317\frac{1}{3}\ =\ 238] minutes.


Tina, then, working by herself would have taken 238 minutes to do the first part and then 272 minutes (4 hrs, 32 minutes) to do the second part for a total of 510 minutes.


But if Tina takes *[tex \Large \frac{3}{4}] of the time the apprentice takes, then the apprentice takes *[tex \Large \frac{4}{3}] of the time that Tina takes.  So the apprentice would take:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4}{3}\ \times\ 510\ =\ 680] minutes or 11 hours, 20 minutes.


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