Let's break down Elena's biking activity into two parts based on the given information:

1. First 5 minutes:

   • Elena bikes at a speed of 15 miles per hour.
   • Time spent: 5 minutes = $\frac{5}{60}$ hours = $\frac{1}{12}$ hours.

   The distance $D_1$ for the first part can be calculated using the formula: $D_1 = \text{Speed} \times \text{Time} = 15 \times \frac{1}{12} = \frac{15}{12} = 1.25 \, \text{miles}$

2. Last 15 minutes:

   • Elena bikes at a speed of 12 miles per hour.
   • Time spent: 15 minutes = $\frac{15}{60}$ hours = $\frac{1}{4}$ hours.

   The distance $D_2$ for the second part can be calculated using the formula: $D_2 = \text{Speed} \times \text{Time} = 12 \times \frac{1}{4} = 3 \, \text{miles}$

To find the total distance $D$ that Elena bikes each day, we add the distances from both parts:

$D = D_1 + D_2 = 1.25 + 3 = 4.25 \, \text{miles}$

Thus, the equation for the total distance $D$ based on her biking routine is:

$D = 4.25$

This means that, regardless of her speed, the total distance she bikes each day is always 4.25 miles.

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Would you like more details or have any questions about this solution?

Here are some related questions that might interest you:

1. How do we convert minutes to hours in other time-based problems?
2. Can you explain how to calculate average speed over the entire 20 minutes?
3. How would the equation change if Elena biked at different speeds on different days?
4. What if Elena took a 5-minute break in between? How would that affect the distance?
5. How would the distance change if she increased her speed for the entire 20 minutes?

Tip: Always remember to convert units (like minutes to hours) properly when calculating rates like speed and distance to maintain consistency.