Question 157341
The solution is to add two rates:
(1) Sarah's rate of walking
(2) The sidewalk's rate of moving
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Added together, these rates equal 
the rate of Sarah walking on the 
moving sidewalk.
Call the length in the problem{{{L}}}
Sarah's rate of walking = {{{L/8}}} length/min
Sidewalk's rate of moving = {{{L/6}}} length/min
Added together: {{{L/8 + L/6}}}
Let {{{t}}} = number of minutes for Sarah to
travel length {{{L}}} when sidewalk is moving
{{{L/8 + L/6 = L/t}}}
Notice I can divide both sides of this equation
by {{{L}}}, resulting in:
{{{1/8 + 1/6 = 1/t}}}
multiply both sides by {{{24t}}}
{{{3t + 4t = 24}}}
{{{7t = 24}}}
{{{t = 3.429}}} min