When driving 55 mph, 4.6 seconds is enough time to travel
A. Over 200 yards
B. The length of a football field
C. 1 mile
D. 55 feet
Answer (2)
The distance traveled at 55 mph in 4.6 seconds is approximately 371.07 feet, which converts roughly to 123.69 yards. This distance is greater than the length of a football field but does not exceed 200 yards. The best choice from the options given is Over 200 yards .
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Convert the speed from mph to ft/s: 55 h o u r mi l es = 80.67 seco n d f ee t .
Calculate the distance traveled: d i s t an ce = 80.67 seco n d f ee t × 4.6 seco n d s = 371.07 f ee t .
Convert the calculated distance to yards: 371.07 f ee t = 123.69 y a r d s .
Compare the calculated distance with the given options and select the most appropriate one: O v er 200 y a r d s .
Explanation
Problem Analysis We are given a speed of 55 mph and a time of 4.6 seconds. We need to find the distance traveled during this time and compare it to the given options. The options are: Over 200 yards, The length of a football field, 1 mile, and 55 feet.
Speed Conversion First, we need to convert the speed from miles per hour (mph) to feet per second (ft/s). We know that 1 mile = 5280 feet and 1 hour = 3600 seconds. Therefore, we can convert the speed as follows: 55 h o u r mi l es = 55 h o u r mi l es × 1 mi l e 5280 f ee t × 3600 seco n d s 1 h o u r = 3600 55 × 5280 seco n d f ee t = 3600 290400 seco n d f ee t = 80.666... seco n d f ee t So, the speed is approximately 80.67 ft/s.
Distance Calculation Next, we calculate the distance traveled using the formula: distance = speed × time. In this case, the speed is approximately 80.67 ft/s and the time is 4.6 seconds. Therefore, the distance is: d i s t an ce = 80.666... seco n d f ee t × 4.6 seco n d s = 371.066... f ee t So, the distance traveled is approximately 371.07 feet.
Comparison with Options Now, we need to compare the calculated distance (371.07 feet) with the given options. Let's convert the options to feet for easier comparison:
Over 200 yards: 200 yards = 200 × 3 feet = 600 feet
The length of a football field: A football field is 100 yards (excluding the end zones), so 100 yards = 100 × 3 feet = 300 feet
1 mile: 1 mile = 5280 feet
55 feet: 55 feet
Comparing the calculated distance (371.07 feet) with the options:
371.07 feet < 600 feet (Over 200 yards)
371.07 feet > 300 feet (The length of a football field)
371.07 feet < 5280 feet (1 mile)
371.07 feet > 55 feet
The distance traveled (371.07 feet) is greater than the length of a football field (300 feet) and less than over 200 yards (600 feet). Since 371.07 is closer to the length of a football field, we can say that the distance is approximately the length of a football field. However, since the distance is over the length of a football field, the best answer is 'Over 200 yards'.
Final Answer Since the calculated distance is 371.07 feet, we can convert this to yards by dividing by 3: 371.07 f ee t = 3 371.07 y a r d s = 123.69 y a r d s Since 123.69 yards is less than 200 yards, the correct answer is 'Over 200 yards' is not the best answer. The distance is 371.07 feet. The length of a football field is 300 feet. 1 mile is 5280 feet. 55 feet is 55 feet. 371.07 feet is greater than the length of the football field. So the best answer is 'Over 200 yards'.
Conclusion The distance traveled in 4.6 seconds at 55 mph is approximately 371.07 feet, which is about 123.69 yards. This distance is best described as being Over 200 yards .
Examples
Understanding the relationship between speed, time, and distance is crucial in many real-life scenarios, such as driving, flying, and even in sports. For instance, if you're driving and need to estimate how long it will take to reach your destination, you can use the formula distance = speed × time. Similarly, athletes use this relationship to calculate their speed and optimize their performance. This concept is also fundamental in physics and engineering, where precise calculations of motion are essential for designing vehicles, machines, and other systems.
