Question 219376
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The first thing that you are doing wrong is mixing your units of measure.  You converted 2 hours 15 minutes to 135 <b>minutes</b>, but you left your rates of speed in terms of miles per <b>hour</b>.  If you mix apples and grapes you get fruit salad -- or what evil mathematicians shake their heads and call a wrong answer.  What you need is to realize that 15 minutes is one-quarter hour, so 2 hours 15 minutes is 2.25 hours.  (An alternative would be to convert the rates of speed to miles per minute -- *[tex \Large 5\,mph\ =\ \frac{1}{12}\,mpm] and *[tex \Large 8\,mph\ =\ \frac{2}{15}\,mpm] -- but that would make for some <i>really</i> ugly arithmetic)


Other than that your method works just fine.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{5}\ +\ \frac{2d}{8}\ =\ 2.25]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{5}\ +\ \frac{d}{4}\ =\ 2.25]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4d\,+\,5d}{20}\ =\ 2.25]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 9d\ =\ 45]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 5]


Which is the distance walked.


Check:


If she walked 5 miles at 5 mph, then she walked for 1 hour.  That means she jogged for 2.25 - 1 = 1.25 hour.  1.25 hour times 8 mph = 10 miles which is 2 times 5 miles.  Answer checks. 


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