Question 1127557
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Let x be the distance from the car park to work; then 65-x is the distance from the apartment building to the car park.<br>
Betty travels the 65-x miles at 45mph and the x miles at 5mph.  Carl travels the 65-x miles at 40mph and the x miles at 6mph.  The time they take is the same.  So<br>
{{{(65-x)/45+x/5 = (65-x)/40+x/6}}}
{{{(65-x)/45+9x/45 = (195-3x)/120+20x/120}}}
{{{(8x+65)/45 = (17x+195)/120}}}
{{{120(8x+65) = 45(17x+195)}}}
{{{960x+7800 = 765x+8775}}}
{{{195x = 975}}}
{{{x = 5}}}<br>
The total time in hours for Betty is<br>
{{{60/45+5/5 = 4/3+1 = 7/3}}}<br>
The total time for Carl is<br>
{{{60/40+5/6 = 3/2+5/6 = 9/6+5/6 = 14/6 = 7/3}}}<br>
It takes each of then 7/3 hours, or 2 1/3 hours, to get to work.  Since they leave at 6:00am, they arrive at 8:20am.