SOLUTION: I have a word problem that goes as follows "A man alternates between jogging and walking while exercising. He traveled 15 miles during the past 3 hours. He jogs at a rate of 7.5mph

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Question 830206: I have a word problem that goes as follows "A man alternates between jogging and walking while exercising. He traveled 15 miles during the past 3 hours. He jogs at a rate of 7.5mph and walks and a rate of 4mph. How much time, to the nearest hundredth of an hour, did he spend walking and how much time did he spend jogging.
I set it up like this:
J+W=3
7.5J+4W=15 and got .57 hours jogging and 2.43 hours walking. I am not sure if I am using the right method though. I have tried different methods of multiplying the 15 by 3 but those answers didn't make much sense.
thank you!
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A man alternates between jogging and walking while exercising. He traveled 15 miles during the past 3 hours. He jogs at a rate of 7.5mph and walks and a rate of 4mph. How much time, to the nearest hundredth of an hour, did he spend walking and how much time did he spend jogging.
I set it up like this:
--------------------------
J+W=3
7.5J+4W=15
-----
Modify:
4J + 4W = 12
7.5J+4W = 15
-------
Subtract to get:
3.5J = 3
J = 6/7 hrs (time spent jogging)
----
Solve for "W":
J + W = 3
(6/7) + W = (21/7)
W = 15/7 hrs (time spent walking)
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Cheers,
Stan H.
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Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
j time jogging
w time walking

_________________speed_________________time_______________distance
jogging__________7.5___________________j__________________(____)
walking__________4_____________________w__________________(____)
Total_________________________________3_____________________15


highlight_green%28R%2At=d%29 for Rate, time, distance.

_________________speed_________________time_______________distance
jogging__________7.5___________________j__________________((7.5)j)
walking__________4_____________________w__________________(4w)
Total_________________________________3_____________________15

highlight%28j%2Bw=3%29 and highlight%28%287.5%29j%2B4w=15%29
You have the correct equations. That is more than half of the solution process.
You are worried about some "right" method to solve the system of equations. Take your choice: Substitution, Elimination, or Matrix.

Let me assume that you had only a temporary difficulty and that you should try solving the system again and find no trouble.

....
As for what I'd do, my choice is Elimination Method. Multiply the time equation by 4; subtract this equation from the distance equation, and you will have an equation in only the variable, j, and can quickly get the value for j.