Vanna walked at a rate of 2 miles per hour for 10 minutes and then walked at a rate of 3 miles her hour for 5 minutes. what is her average rate in miles per hour for the 15 minute period?

The average rate is 7/3 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- The average rate = total distance ÷ total time

- Vanna walked at rate 2 miles per hour for 10 minutes

- She then walked at a rate 3 miles per hour for 5 minutes

- We wants to know her average rate in mile per hour for the 15

 minutes period

- We must find the distance she walked in the 10 minutes and

  5 minutes

- Remember that the distance = speed × time

∵ 1 hour = 60 minutes

∴ 1 minute = 1/60 hour

∵ She walked at first for 10 minutes

- Change the minutes to hours

∴ She walked for = 10 × 1/60 = 1/6 hour

∵ Her rate (speed) is 2 miles per hour

∴ The distance she walked = 2 × 1/6 = 1/3 miles

∵ She walked at second for 5 minutes

- Change the minutes to hours

∴ She walked for = 5 × 1/60 = 1/12 hour

∵ Her rate (speed) is 3 miles per hour

∴ The distance she walked = 3 × 1/12 = 1/4 miles

∵ The average rate = the total distance ÷ total time

∵ Total distance = 1/3 + 1/4 = 7/12 miles

∵ The total time = 10 + 5 = 15 minutes

- Change the minutes to hours

∵ 15 minutes = 15 × 1/60 = 1/4 hour

∴ The average rate = 7/12 ÷ 1/4 = 7/3 miles/hour

* The average rate is 7/3 miles per hour