Question

Robbi rides her bicycle uphill for three miles at 8 mph. She then rides on level ground for seven miles at 14 mph. She continues downhill for twelve miles at 24 mph. What is her average speed in miles per hour for the entire trip?

Answer 1

To find Robbi's average speed for the trip, we add the total distance traveled and divide by the total time taken. After calculating the time for each segment (3 miles uphill, 7 miles on level ground, and 12 miles downhill), we find the average speed to be 16 mph.

Step-by-step explanation:

To calculate Robbi's average speed for the entire trip, we need to consider the total distance she traveled and the total time she took. The average speed is the total distance divided by the total time. We will calculate the time taken for each part of her trip and then find the total time.

• Uphill: Distance = 3 miles, Speed = 8 mph, Time = 3 mi / 8 mph = 0.375 hours
• Level Ground: Distance = 7 miles, Speed = 14 mph, Time = 7 mi / 14 mph = 0.5 hours
• Downhill: Distance = 12 miles, Speed = 24 mph, Time = 12 mi / 24 mph = 0.5 hours

Total Distance: 3 + 7 + 12 = 22 miles

Total Time: 0.375 + 0.5 + 0.5 = 1.375 hours

Therefore, Robbi's average speed is:

Average Speed = Total Distance / Total Time

Average Speed = 22 miles / 1.375 hours = 16 mph

Answer 2

Average speed of Robbi = 16 mph

Step-by-step explanation:

Formula for the average speed is,

Average speed =
`\frac{\text{Total distance covered}}{\text{Total time taken}}`

Total distance covered by Robbi = 3 + 7 + 12

= 22 miles

Time taken to cover 3 miles =
`\frac{\text{Distance covered}}{\text{Speed}}`

=
`(3)/(8)` hours

= 0.375 hours

Time taken to cover 7 miles =
`(7)/(14)`

= 0.5 hours

Times taken to cover 12 miles =
`(12)/(24)`

= 0.5 hours

Total time taken to cover the entire trip = 0.375 + 0.5 + 0.5

= 1.375 hours

Average speed of Robbi =
`(22)/(1.375)`

= 16 miles per hour