The question involves filling out a tape diagram and determining how long it took a runner to run 15 miles, based on the information that the runner covered 25 miles in 5 hours.

Step-by-step solution:

1. Understand the Problem: The runner's speed (rate) is constant. They ran 25 miles in 5 hours. To find the time for 15 miles, first calculate the rate of running in miles per hour.

2. Calculate the Rate:
   $\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{25 \, \text{miles}}{5 \, \text{hours}} = 5 \, \text{miles per hour}.$

3. Set Up the Diagram: The diagram splits the total time (5 hours) into equal intervals, corresponding to equal distances (5 miles each). Each segment represents 1 hour and 5 miles.

4. Determine Time for 15 Miles:

   • The total distance is split into 5-mile intervals (since the rate is 5 miles/hour).
   • For 15 miles, divide: $\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{15 \, \text{miles}}{5 \, \text{miles per hour}} = 3 \, \text{hours}.$

Fill in the Missing Numbers on the Diagram:

• Time (hours): Each interval corresponds to 1 hour. The numbers will be: $0, 1, 2, 3, 4, 5$.
• Distance (miles): Each interval corresponds to 5 miles. The numbers will be: $0, 5, 10, 15, 20, 25$.

Final Answer:

It took the runner 3 hours to run 15 miles.

Would you like further explanation or additional examples? Here are 5 related questions to expand your understanding:

1. How would you calculate the time if the runner ran 35 miles instead of 25 miles at the same pace?
2. What is the formula for calculating speed, and how can it be rearranged to solve for time or distance?
3. If another runner completed 25 miles in 4 hours, what was their speed, and how does it compare to the first runner's speed?
4. What would the diagram look like if the runner took 10 hours to run 50 miles?
5. How can you represent this problem as a proportion?

Tip: When solving word problems with rates, always ensure units (miles, hours, etc.) are consistent before performing calculations.