SOLUTION: 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. Ho

Question 1190208: 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?
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
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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    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    hours.


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

     =    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 =  = 1.125.


Thus the distance to the school is  1.125 miles,  or  1  miles.          ANSWER


It takes Travis   = 0.125  hours to jog to school, which is 1/8 of an hour, or 7.5 minutes.    ANSWER


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

        1  -  =  =   is exactly 0.5 of a mile, in accordance with the problem.

Solved, explained and checked.

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