Question

Alicia wanted to lose some weight, so she planned a day of exercising. She spent a total of 3 hours riding her bike and jogging. She biked for 12 miles and jogged for 12 miles. Her rate for jogging was 6 mph less than her biking rate. What was her rate when jogging?
Please answer asap thank you :)

Answer 1

Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, hence:

$v = \frac{d}{t}$

Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:

$v = \frac{12}{t}$

Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:

$v + 6 = \frac{12}{3 - t}$

$v = \frac{12}{3 - t} - 6$

Then:

$\frac{12}{t} = \frac{12}{3 - t} - 6$

$\frac{12}{3 - t} - \frac{12}{t} = 6$

$\frac{12t - 36 + 12t}{t(3 - t)} = 6$

18t - 6t² = 24t - 36

6t² + 6t - 36 = 0

t² + t - 6 = 0

(t + 3)(t - 2) = 0. -> t = 2 hours.

Hence her jogging rate in mph is given as follows:

$v = \frac{12}{2} = 6$

More can be learned about the relation between velocity, distance and time at brainly.com/question/24316569

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