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Answer :
To determine the average speed for the 8.00-mile trip, and if it is greater than, less than, or equal to 40.0 mi/h, let's break it down into steps:
1. Understand the problem:
- You're driving two segments:
- First segment: 4.00 miles at 30.0 miles per hour.
- Second segment: 4.00 miles at 50.0 miles per hour.
2. Calculate the time for each segment:
- Time for the first segment is calculated as distance divided by speed:
- Time 1 = 4.00 miles / 30.0 mi/h = 0.1333 hours
- Time for the second segment:
- Time 2 = 4.00 miles / 50.0 mi/h = 0.08 hours
3. Calculate the total time for the trip:
- Total time = Time 1 + Time 2 = 0.1333 hours + 0.08 hours = 0.2133 hours
4. Calculate the total distance of the trip:
- Total distance = 4.00 miles + 4.00 miles = 8.00 miles
5. Calculate the average speed for the entire trip:
- Average speed = Total distance / Total time = 8.00 miles / 0.2133 hours = 37.5 mi/h
6. Compare the average speed with 40.0 mi/h:
- Since 37.5 mi/h is less than 40.0 mi/h, the average speed for the trip is less than 40.0 mi/h.
So, the average speed for your 8.00-mile trip is less than 40.0 mi/h. This is because the total time you spend during slower segments has a greater impact on the average speed, given the same distance is covered in each segment.
1. Understand the problem:
- You're driving two segments:
- First segment: 4.00 miles at 30.0 miles per hour.
- Second segment: 4.00 miles at 50.0 miles per hour.
2. Calculate the time for each segment:
- Time for the first segment is calculated as distance divided by speed:
- Time 1 = 4.00 miles / 30.0 mi/h = 0.1333 hours
- Time for the second segment:
- Time 2 = 4.00 miles / 50.0 mi/h = 0.08 hours
3. Calculate the total time for the trip:
- Total time = Time 1 + Time 2 = 0.1333 hours + 0.08 hours = 0.2133 hours
4. Calculate the total distance of the trip:
- Total distance = 4.00 miles + 4.00 miles = 8.00 miles
5. Calculate the average speed for the entire trip:
- Average speed = Total distance / Total time = 8.00 miles / 0.2133 hours = 37.5 mi/h
6. Compare the average speed with 40.0 mi/h:
- Since 37.5 mi/h is less than 40.0 mi/h, the average speed for the trip is less than 40.0 mi/h.
So, the average speed for your 8.00-mile trip is less than 40.0 mi/h. This is because the total time you spend during slower segments has a greater impact on the average speed, given the same distance is covered in each segment.
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