A bicyclist started riding at 8:00 a.m. The diagram below shows the distance the bicyclist had traveled at different times.
What was the bicyclist's average rate of speed in miles per hour?
- 8:00 a.m. at 4.5 miles
- 8:15 a.m. at 7.5 miles
- 8:45 a.m.
Answer (3)
The overall average rate of speed of the bicyclist is 26.67 miles per hour.
Explaination:
The problem presented to us requires us to calculate the average rate of speed of a bicyclist who started riding at 8:00 a.m. The given information includes the distance traveled by the bicyclist at different times, which is represented in the diagram below. To find the average rate of speed during each interval, we use the formula for average rate of speed, which is total distance traveled divided by total time taken. During the first interval from 8:00 a.m. To 8:15 a.m., the bicyclist covered a distance of 4.5 miles. During this time, we assume that the bicyclist was traveling at a constant speed, which means that the time taken to cover this distance is also constant. Therefore, we can calculate the average rate of speed during this interval as follows:
Average rate of speed from 8:00 a.m. To 8:15 a.m. = Total distance traveled / Total time taken
= (7.5 miles - 4.5 miles) / (00:15 minutes - 00:00 minutes)
= 3 miles / 00:15 minutes
= 20 miles per hour (rounded off)
During the second interval from 8:15 a.m. To 8:45 a.m., the bicyclist covered a distance of 7.5 miles. Again, we assume that the bicyclist was traveling at a constant speed during this time interval as well, and we can calculate the average rate of speed during this interval as follows:
Average rate of speed from 8:15 a.m. To 8:45 a.m. = Total distance traveled / Total time taken
= (12 miles - 7.5 miles) / (00:30 minutes - 00:15 minutes)
= 4.5 miles / 00:15 minutes
= 30 miles per hour (rounded off)
To find the overall average rate of speed for the entire duration, we need to add up all the distances traveled and divide it by the total time taken. The total distance traveled is 12 miles, and the total time taken is (8:45 a.m. - 8:00 a.m.) or (12:45 p.m. - 8:00 a.m.) or (04:45 hours). Therefore, we can calculate the overall average rate of speed as follows:
Overall average rate of speed = Total distance traveled / Total time taken
= 12 miles / 04:45 hours
= 26.67 miles per hour (rounded off)
In conclusion, by using the formula for average rate of speed and making assumptions about constant speeds during each interval, we were able to calculate both the average rates of speed during each interval and the overall average rate of speed for the entire duration provided in this problem statement. This calculation helps us understand how efficiently the bicyclist was able to cover a certain distance in a specific amount of time, which can be useful in planning future journeys accordingly or analyzing performance data for athletes or commuters who use bicycles as their primary mode of transportation over long distances or during competitions where timing is critical for success. ;
The bicyclist's average rate of speed between 8:00 a.m. and 8:15 a.m. was determined to be 12 miles per hour by calculating the distance traveled divided by the time taken, after converting minutes to hours. ;
The bicyclist's average rate of speed is calculated to be 10 miles per hour, determined by finding the total distance traveled and the total time taken during the ride. The distances covered were 3 miles in the first interval and 4.5 miles in the second interval, taking a total of 0.75 hours. Thus, by dividing the total distance by the total time, we achieve the average speed.
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