SOLUTION: 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 a

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 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 a      Log On


   

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?
Found 3 solutions by josgarithmetic, ikleyn, Alan3354:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
              SPEEDS             TIME                      DISTANCE

WALKING           5              13/20-x                    5(13/20-x)

RUNNING          12               x                         12x

SUMS                            39minutes=(39/60)hour         5
                                          (13/20)hour

Your question asked for a system, but the problem description can be handled with one variable. If you really wanted, you could give another variable to the walking time.

highlight_green%2813%2F4-5x%2B12x=5%29
5-13%2F4=7x
7x=5-13%2F4
28x=20-13
28x=7
highlight%28x=1%2F4%29----------------Fifteen minutes running.
highlight%2824_MINUTES%29------------------Twenty-four minutes walking.

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~ 


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%2F60 of an hour

      %285-x%29%2F5    +    x%2F12      = 39%2F60.


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.


ANSWER.  3 kilometer running and (5-3) = 2 kilometers walking.

Solved.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How far did the person run for? How long did the person walk for?
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Why for?
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How far did the person run? How long did the person walk?