Question 31768
<pre><b>Let Dan's pace be x
let Julio's pace be x-10
Total propotion:
{{{1/(x-10)+1/x=1/12}}}
Cross multiply:
*[tex (x-10)+(x)=\frac{(x)(x-10)}{12}]
{{{2x-10=(x^2-10x)/12}}}
Multiply the whole equation by 12 to remove the fraction:
{{{12(2x/1)-12(10/1)=12((x^2-10x)/12)}}}
Simplfy:
{{{24x-120=x^2-10x}}}
Put it into *[tex ax^2+bx+c] form:
{{{x^2-34x+120=0}}}
Use the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In which a=1, b=-34, c=120
{{{x = (-(-34) +- sqrt( (-34)^2-4*1*120 ))/(2*1) }}} 
Remove the negative sign:
{{{x=(34+sqrt(1156-480))/2}}}
{{{x=(34+26)/2}}}
x=30
30-10=20
<font color = brown>Hence, Julio can mow the lawn is 20 minuites and Dan can mow the lawn is 30 minutes when working alone.</font>
Paul.