Using a system of equations, it is found that:
a) Suzette ran for 2 hours.
b) Suzette biked for 2 hours.
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Velocity is distance divided by time, thus:
[tex]v = \frac{d}{t}[/tex]
- Running, the distance was d, the velocity was [tex]v = 6[/tex] and the time was t. Thus
[tex]6 = \frac{d}{t}[/tex]
[tex]d = 6t[/tex]
- Biking, the distance was 36 - d, the velocity was [tex]v = 12[/tex] and the time was 4 - t. Thus
[tex]v = \frac{d}{t}[/tex]
[tex]12 = \frac{36 - d}{4 - t}[/tex]
The substitution is:
[tex]d = 6t[/tex]
Then, on the second equation:
[tex]12 = \frac{36 - 6t}{4 - t}[/tex]
[tex]36 - 6t = 48 - 12t[/tex]
[tex]6t = 12[/tex]
[tex]t = \frac{12}{6}[/tex]
[tex]t = 2[/tex]
- Thus, she ran for 2 hours, as [tex]t = 2[/tex] and biked for 2 hours, as [tex]4 - t = 4 - 2 = 2[/tex].
A similar problem is given at https://brainly.com/question/24316569
