Respuesta :
Using the relationship between velocity, distance and time, it is found that Red Riding Hood drives at 54 mph.
What is the relation between velocity, distance and time?
Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
Red Riding Hood drives the 432 miles to Grandmother’s house in 1 hour less than it takes the Wolf to drive the same route, at a speed of 6 mph faster, hence the equations are:
[tex]v = \frac{432}{t}[/tex]
[tex]v + 6 = \frac{432}{t - 1}[/tex]
From the first equation:
[tex]t = \frac{432}{v}[/tex]
Replacing on the second equation:
[tex]v + 6 = \frac{432}{t - 1}[/tex]
[tex]v + 6 = \frac{432}{\frac{432}{v} - 1}[/tex]
[tex]v + 6 = \frac{432v}{432 - v}[/tex]
[tex]432v - v^2 + 2592 - 6v = 432v[/tex]
[tex]v^2 + 6v - 2592 = 0[/tex]
(v + 54)(v - 48) = 0.
The velocity is positive, hence:
v - 48 = 0 -> v = 48 mph.
Red Riding Hood drives 6 mph faster than Wolf, hence:
v + 6 = 48 + 6 = 54 mph.
More can be learned about the relationship between velocity, distance and time at https://brainly.com/question/24316569
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