Question 1127557
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Let x be the distance from the apartment building to the parking.


Then we have the time equation


    <U>Betty's total travel time</U>  =  <U>Carl's total travel rime</U>


    {{{x/45 + (65-x)/5}}}                  =  {{{x/40 + (65-x)/6}}}


Multiply both sides by 45*5*40*6


    5*40*6x + 45*40*6*(65-x) = 45*5*6*x + 45*5*40*(65-x)

    5*40*6x - 45*40*6x - 45*5*6x + 45*5*40x = 45*5*40*65 - 45*40*6*65

    (5*40*6 - 45*40*6 - 45*5*6 + 45*5*40)x = 45*5*40*65 - 45*40*6*65

    -1950x = -117000

    x = {{(-117000)/(-1950)}}} = 60.


Thus we found the distance x = 60 miles.


Hence, Betty spends  {{{60/45}}} + {{{5/5}}} hours = 1 hour 20 minutes + 1 hour = 2 hours and 20 minutes.


To check, Carl spends the same time  {{{60/40}}} + {{{5/6}}} hours = 1 hour 30 minutes + 50 minutes = 2 hours and 20 minutes.


Hence, they both arrive to work at 8:20 am.
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