Jane decided she wanted to retire from being in the Math Saxon books. To celebrate, she baked 7,893 cookies for her and Homeratho. Unfortunately, her obese turtle ate one third of them. Now she had to bake more cookies. Homeratho was coming back home after eating a burger, and Jane needed to finish the cookies fast. If Homeratho was coming back home at 2 miles per hour and was 10 miles away from home, at what rate would Jane need to bake the remaining cookies? BONUS QUESTION: What if Homeratho was feeling extra lazy and decided to take a train that travels at 200 miles per hour to get home, what rate would Jane need to bake the cookies if she wanted to finish them all in time?

To solve both the original question and the bonus question, we’ll follow a logical sequence of steps:

### Part 1: Rate for Original Scenario

1. **Calculate the remaining cookies after the turtle ate one-third:**

   Jane originally baked 7,893 cookies. The turtle ate one-third of them.

   \[
   \text{Cookies eaten by turtle} = \frac{1}{3} \times 7893 = 2631
   \]

   Thus, the remaining cookies are:

   \[
   \text{Remaining cookies} = 7893 - 2631 = 5262
   \]

2. **Determine how long Homeratho takes to reach home:**

   Homeratho is 10 miles away and traveling at 2 miles per hour.

   \[
   \text{Time to reach home} = \frac{10 \text{ miles}}{2 \text{ miles per hour}} = 5 \text{ hours}
   \]

3. **Calculate the baking rate Jane needs:**

   Jane must bake 2,631 cookies (the cookies eaten by the turtle) in 5 hours.

   \[
   \text{Baking rate} = \frac{2631 \text{ cookies}}{5 \text{ hours}} = 526.2 \text{ cookies per hour}
   \]

### Part 2: Rate for Bonus Scenario

Now, let’s solve for the bonus scenario where Homeratho takes a train at 200 miles per hour.

1. **Calculate the time for Homeratho to reach home on the train:**

   Homeratho is still 10 miles away, but now he’s traveling at 200 miles per hour.

   \[
   \text{Time to reach home} = \frac{10 \text{ miles}}{200 \text{ miles per hour}} = 0.05 \text{ hours} = 3 \text{ minutes}
   \]

2. **Calculate the new baking rate:**

   Jane still needs to bake 2,631 cookies, but now she only has 3 minutes (or 0.05 hours) to do so.

   \[
   \text{Baking rate} = \frac{2631 \text{ cookies}}{0.05 \text{ hours}} = 52620 \text{ cookies per hour}
   \]

### Conclusion:
- In the original scenario, Jane needs to bake at a rate of **526.2 cookies per hour**.
- In the bonus scenario (if Homeratho takes the train), Jane would need to bake at an extremely high rate of **52,620 cookies per hour** to finish in time.

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Would you like more details or have any questions? Here are five related questions:

1. What if Homeratho were 15 miles away instead of 10 miles in the original scenario? How would that affect the baking rate?
2. What would happen if Jane could only bake 500 cookies per hour? Could she finish on time in the original scenario?
3. How much time would Homeratho save by taking the train compared to walking?
4. If Jane baked an additional 1,000 cookies before the turtle ate one-third, how would that change the required baking rate?
5. What would be the total time Jane would need if she could only bake 400 cookies per hour?

**Tip:** When calculating baking rates or any other rates, always double-check the time conversions (hours, minutes) to ensure accuracy.

Learn how to calculate the baking rate for Jane's cookies problem where she needs to bake cookies at a specific rate to meet Homeratho's arrival time. Includes solutions for both walking and train scenarios. Suitable for students in Grades 5-7.

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