SOLUTION: Please help me. I have been working on this problem with a classmate of mine and we cant figure this one out at all. We were thinking.... x + y = 6 and 8x + 3y = 60 However, th

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Question 153852: Please help me. I have been working on this problem with a classmate of mine and we cant figure this one out at all.
We were thinking.... x + y = 6 and 8x + 3y = 60 However, thats not correct.
Lisa Chung wants to cover a 6 miles course in 1 hour by running part of the way and walking the rest. She also wants to make a 5 minute stop for water. Lisa runs 8 mph and walks 3 mph. How many miles will she have to run?
Please help and as always - I do appreciate you.

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Lisa Chung wants to cover a 6 miles course in 1 hour by running part of the way and walking the rest. She also wants to make a 5 minute stop for water. Lisa runs 8 mph and walks 3 mph. How many miles will she have to run?
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Let "x" be the miles Lisa runs; Then she will walk "6-x" miles.
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Her running time: distance/rate = x/8 hrs
Her walking time: distance/rate = (6-x)/3 hrs
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EQUATION
run time + walk time + (5/60)water time = 1 hr
x/8 + (6-x)/3 + (5/60) = 1
Multiply thru 120:
15x + 40(6-x) + 10 = 120
15x + 240 - 40x + 10 = 120
25x = 130
x = 5.2 miles (distance she must run)
6-x = 0.8 miles (distance she must walk)
=======================
Cheers,
Stan H.

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution:
Please help me. I have been working on this problem with a classmate of mine and we cant figure this one out at all.
We were thinking.... x + y = 6 and 8x + 3y = 60 However, thats not correct.
Lisa Chung wants to cover a 6 miles course in 1 hour by running part of the way and walking the rest. She also wants to make a 5 minute stop for water. Lisa runs 8 mph and walks 3 mph. How many miles will she have to run?
Please help and as always - I do appreciate you. 

Your second equation is wrong.

Let x = the distance she runs
Ley y = the distance she walks

x + y = 6

That's the distance equation.

Now we must make a time equation.

We must use TIME=%28DISTANCE%29%2F%28RATE%29, not "distance times rate".

The time she runs = x%2F8

The time she walks = y%2F3

Now since she stops to rest 5 minutes, the total time
she walks and runs is only 55 minutes.  But we must change
55 minute to hours by dividing it by 60.  So the total
time is 55%2F60ths of an hour, which reduces to 11%2F12ths
of an hour.  So the second equation is

x%2F8%2By%2F3+=+11%2F12

Then we clear that of fractions by multiplying
through by the LCD 24%2F1

%2824%2F1%29%28x%2F8%29%2B%2824%2F1%29%28y%2F3%29+=+%2824%2F1%29%2811%2F12%29


  3      8           2


3x%2B8y=22

So the system to solve is

system%28x%2By=6%2C3x%2B8y=22%29

Multiply the first equation through by -3
to eliminate the x's.  Add vertically term 
by term:

-3x - 3y = -18
 3x + 8y =  22
--------------
      5y = 4
       y = 4%2F5ths of a mile she runs.

system%28x%2By=6%2C3x%2B8y=22%29

Now multiply the first equation through by -8
to eliminate the y's.  Add vertically term by term:

-8x - 8y = -48
 3x + 8y =  22
--------------
-5x      = -26
  x      = %28-26%29%2F%28-5%29
       x = 26%2F5 = 51%2F5miles she walks. 

Edwin