Question 1189539
.
A person leaves their work and heads home 5km away. 
They walk at 5km/h during the start but then it starts to rain 
so they run the rest of the way at 12km/h. 
They leave at 5:30pm and arrives home at 6:09 pm. 
Create a system of equations. 
How far did the person run for? How long did the person walk for?
~~~~~~~~~~~~~~~



<pre>
Let x be the distance the person ran, in kilometers.

Then the distance he walked was (5-x) kilometers.


Now write the "time equation"

    time to walk + time to run = 39 minutes, or {{{39/60}}} of an hour

      {{{(5-x)/5}}}    +    {{{x/12}}}      = {{{39/60}}}.


To solve it, multiply both sides by 5*12 = 60.  You will get

    12*(5-x) + 5x = 39

    60 - 12x + 5x = 39

    60 - 39 = 7x

      21    = 7x

       x    = 21/7 = 3.


<U>ANSWER</U>.  3 kilometer running and (5-3) = 2 kilometers walking.
</pre>

Solved.