To calculate Jana's average rate for the first part of the race, we can use the formula for average speed:

$\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}$

Step-by-step solution:

1. Distance traveled: Jana ran $\frac{3}{12}$ miles, which simplifies to $\frac{1}{4}$ miles.
2. Time taken: She ran for $\frac{1}{3}$ hour.
3. Calculate the average speed: Plugging the values into the formula:

$\text{Average Speed} = \frac{\frac{1}{4} \, \text{miles}}{\frac{1}{3} \, \text{hours}} = \frac{1}{4} \times \frac{3}{1} = \frac{3}{4} \, \text{miles per hour}$

Thus, Jana's average rate for the first part of the race was $\frac{3}{4}$ miles per hour, or 0.75 miles per hour.

Explanation:

I solved this by:

• Converting the distance to a fraction.
• Using the average speed formula.
• Simplifying the fraction to get the final rate.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How would her average speed change if she ran $\frac{1}{2}$ mile in $\frac{1}{3}$ hour?
2. How long would it take her to finish the entire 5-mile race at the same average speed?
3. What is the formula for average speed if we include acceleration?
4. If she took twice as long, what would her new speed be?
5. How would you calculate her speed if she ran the first mile in a different time?

Tip: When calculating average rates, always ensure you use the same units for both distance and time.