Math Problem Statement

On a bicycle, Janet rides for 2 hours and is 14 miles from her house. After riding for 12 hours, she is 74 miles away. What is Janet's rate?

Solution

We are given that Janet rides for:

  1. 2 hours and covers 14 miles.
  2. After 12 hours of total riding, she is 74 miles away.

To find Janet's rate of speed (miles per hour), we can calculate it as follows:

  1. In the first 2 hours, she rides 14 miles, so her rate for that portion is: 14 miles2 hours=7 miles per hour\frac{14 \text{ miles}}{2 \text{ hours}} = 7 \text{ miles per hour}

This suggests that Janet is riding at a constant speed of 7 miles per hour.

Would you like more details or clarifications?

Here are five related questions:

  1. How would her rate change if she covered a different distance in the first 2 hours?
  2. What would her total distance be after 15 hours at this rate?
  3. How long would it take her to cover 100 miles at the same speed?
  4. What is the average speed if she traveled different speeds over different intervals?
  5. If she started from 10 miles away from her house, how would her distance be affected after 2 hours?

Tip: Always remember that speed is the distance traveled divided by the time taken, and it's assumed constant unless specified otherwise!

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Math Problem Analysis

Mathematical Concepts

Distance, Speed, and Time

Formulas

Rate = Distance / Time

Theorems

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Suitable Grade Level

Grade 6-8