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Suzette ran and biked for a total of 36 miles in 4 h. Her average running speed was 6 mph and her average biking speed was 12 mph.
Let x = total hours Suzette ran.
Let y = total hours Suzette biked.
Use substitution to solve for x and y. Show your work. Check your solution.
(a) How many hours did Suzette run?
(b) How many hours did she bike?

Answer :

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].

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