Question 153852
<font size = 6 color = "red"><b>Edwin's solution:</font></b>

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. 
<pre><font size = 4 color = "indigo"><b>
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=(DISTANCE)/(RATE)}}}, not "distance times rate".

The time she runs = {{{x/8}}}

The time she walks = {{{y/3}}}

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 {{{55/60}}}ths of an hour, which reduces to {{{11/12}}}ths
of an hour.  So the second equation is

{{{x/8+y/3 = 11/12}}}

Then we clear that of fractions by multiplying
through by the LCD {{{24/1}}}

{{{(24/1)(x/8)+(24/1)(y/3) = (24/1)(11/12)}}}


  {{{3}}}      {{{8}}}           {{{2}}}
{{{(cross(24)/1)(x/cross(8))+(cross(24)/1)(y/cross(3)) = (cross(24)/1)(11/cross(12))}}}

{{{3x+8y=22}}}

So the system to solve is

{{{system(x+y=6,3x+8y=22)}}}

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 = {{{4/5}}}ths of a mile she runs.

{{{system(x+y=6,3x+8y=22)}}}

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      = {{{(-26)/(-5)}}}
       x = {{{26/5}}} = {{{5}}}{{{1/5}}}miles she walks. 

Edwin</pre>