Let's call Maria's average speed [tex]M[/tex]
Imagine for a moment that Maria has a stopwatch, that measures in hours.
She starts her stopwatch when she starts driving.
If Maria looks at her stopwatch at a time [tex]t[/tex], her distance traveled will be [tex]M * t[/tex] miles. (This is true since [tex]distance = speed * time[/tex].)
What about Ralph? If Ralph could look at Maria's stopwatch, his distance traveled would be [tex]40*t + 6[/tex], since his speed is 40mph and he got a six-mile head start. Remember that [tex]t[/tex] is measured from Maria's start, not Ralph's.
So when they meet, after 1.5 hours, their distances are equal. So:
[tex]Distance(Maria) = Distance(Ralph)[/tex]
[tex]M*t=40t+6[/tex]
And since that time is 1.5, we plug that in for t:
[tex]M*1.5=40*1.5+6[/tex]
[tex]M*1.5=60+6[/tex]
[tex]M*1.5=66[/tex]
Divide both sides by 1.5:
[tex]\frac{M*1.5}{1.5} =\frac{66}{1.5} [/tex]
Which cancels on the left:
[tex]M = \frac{66}{1.5} = 44[/tex] miles per hour.
