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