distance = rate*time
convert minutes to hour first because the question talking about 15 mile per hour
40 mins = 40/60 2/3 hrs
30 mins = 30/60 = 1/2hrs
Assume that s be the speed when Fritz driving, so
s + 15 will be the speed of the train.
We know the time we know the speed, Next
distance that Fritz drive = [tex] \frac{2}{3}s[/tex]
distance the train travel = [tex] \frac{1}{2}(s+15)[/tex]
The question: Assume that the train travels the same distance as the car
==> [tex] \frac{2}{3}s = \frac{1}{2}(s+15)[/tex]
==> [tex] \frac{2}{3}s = \frac{1}{2}s + \frac{15}{2}[/tex]
==> [tex] \frac{2}{3}s - \frac{1}{2}s = \frac{15}{2}[/tex]
==> [tex] \frac{1}{6}s = \frac{15}{2}[/tex]
==> [tex] \frac{6}{1} * \frac{1}{6}s = \frac{15}{2} * \frac{6}{1}[/tex]
==> [tex] s = 45 [/tex]
Now we know that Fritz drive at 45 mph,
distance = [tex] \frac{2}{3} * 45 = 30 miles [/tex]
