Question 1190208
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Travis and his sister Kate jog to school daily. 
Travis jogs at 9 miles per hour, and Kate jogs at 5 miles per hour. 
When Travis reaches school, Kate is 1/2 mile from the school. 
How far do Travis and Kate live from their school? How long does it take Travis to jog to school?
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Let d be the distance to the school (in miles).


Travis jogged d miles in  {{{d/9}}}  hours (to find the time, we divide the distanse by the rate).


At the same time,  Kate jogged  d-0.5 miles;  her time jogging  was  {{{(d-0.5)/5}}}  hours.


The Travis' time is the same as the Kate time, so we write this "time" equation

    {{{d/9}}} = {{{(d-0.5)/5}}}   hours.


To solve it, multiply both sides by 45.  You will get

    5d = 9*(d-0.5)


Simplfy and find d

    5d = 9d - 4.5

    4.5 = 9d - 5d 

    4.5 =   4d

    d = {{{4.5/4}}} = 1.125.


Thus the distance to the school is  1.125 miles,  or  1 {{{1/8}}} miles.          <U>ANSWER</U>


It takes Travis  {{{1.125/9}}} = 0.125  hours to jog to school, which is 1/8 of an hour, or 7.5 minutes.    <U>ANSWER</U>


<U>CHECK</U>.  In 1/8 of an hour, Kate jogged  5/8 of a mile, and the difference  

        1 {{{1/8}}} - {{{5/8}}} = {{{9/8-5/8}}} = {{{4/8}}}  is exactly 0.5 of a mile, in accordance with the problem.
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Solved, explained and checked.