A Car Left Point A at 730 AM Average Speed Solved

Struggling with the “a car left point A at 7:30 am” math problem? You’re not alone; many students find distance-rate-time word problems tricky. This specific question is a classic example designed to test your understanding of average speed.

The average speed of the car was 54 miles per hour (mph). This correct solution is found by first calculating the total travel time, which is 3 hours, and then dividing the total distance of 162 miles by that time.

Based on a thorough analysis of standard mathematical formulas, this guide provides the verified solution. You will discover the exact step-by-step process to solve this problem correctly. We will also explore why a common incorrect answer is wrong, ensuring you master the concept for good.

Key Facts

• The Core Formula is Invariable: The solution always relies on the standard formula: Average Speed = Total Distance / Total Time.
• Total Travel Time is 3 Hours: The elapsed time from the departure at 7:30 AM to the arrival at 10:30 AM is exactly three hours.
• Total Distance is 162 Miles: The problem explicitly states the car traveled a total distance of 162 miles from Point A to Point B.
• The Verified Answer is 54 MPH: Accurate computation shows that dividing 162 miles by 3 hours results in an average speed of 54 miles per hour.
• Units are Critical: The final answer must be expressed in the correct units, miles per hour (mph), which are derived from the units used for distance (miles) and time (hours).

What Was the Average Speed of a Car That Left Point A at 7:30 AM and Arrived at Point B, 162 Miles Away, at 10:30 AM?

The verified solution to this problem is that the car’s average speed was 54 miles per hour (mph). This is the definitive and correct answer derived from the fundamental principles of kinematics. This type of word problem, a common feature in algebra and physics curricula, is designed to assess your ability to extract key data and apply the correct formula.

Many search results or test options might suggest incorrect answers, but the mathematical proof is straightforward. By breaking down the problem into simple, logical steps, you can confidently arrive at the correct solution and understand the process behind it. This ensures you are prepared for similar quantitative reasoning questions on homework or standardized tests.

How Do You Calculate the Average Speed for the Car’s Journey?

To solve the problem, you follow a clear, four-step process: determine the total travel time, identify the total distance, apply the average speed formula, and calculate the final answer. This methodical approach ensures accuracy and removes the guesswork from solving distance-rate-time problems. Each step builds upon the last, leading you directly to the correct solution.

Step 1: How Do You Determine the Total Travel Time?

First, you must find out how long the car was on the road. The problem states the car left at 7:30 AM and arrived at 10:30 AM. You find the total travel time by subtracting the departure time from the arrival time.

The calculation is simple: 10:30 AM – 7:30 AM = 3 hours. The car’s journey took exactly 3 hours. This value for ‘Total Time’ is the first piece of information you need for the main formula.

Step 2: What Is the Total Distance Traveled?

The next step in any word problem is to identify the known values given to you. In this case, the problem statement is direct. It tells you that the car traveled from Point A to Point B, which are 162 miles away from each other.

Therefore, the ‘Total Distance’ is 162 miles. There is no hidden calculation needed for this step; you simply extract the value from the text. Now you have the second piece of the puzzle.

Step 3: What Is the Formula for Average Speed?

With the time and distance known, you need the correct tool to connect them. The standard formula for calculating average speed is one of the most fundamental equations in both math and physics. It defines the relationship between these three quantities.

Average Speed = Total Distance / Total Time

This formula tells you that to find the average speed, you divide the total distance covered by the total amount of time the journey took. Think of it as figuring out how many miles were covered, on average, within each hour of the trip.

Step 4: How Do You Calculate the Final Answer?

Now, you put all the pieces together. You take the values you identified in the first two steps and plug them into the formula from Step 3.

• Total Distance = 162 miles
• Total Time = 3 hours

The calculation is: 162 miles ÷ 3 hours = 54.

And that’s it! By following these steps, you have successfully solved the problem. The final answer, including the proper units, is 54 mph.

Why Is the Correct Answer 54 MPH and Not 53 MPH?

The correct answer is 54 mph because the mathematical division of 162 miles by 3 hours is exactly 54. The figure of 53 mph is a common calculation error or a “distractor” answer often used in multiple-choice questions to test if you have performed the division accurately.

Trusting the formula and performing a simple verification check is the best way to avoid this mistake. The relationship between distance, speed, and time is absolute. If you multiply the correct speed (54 mph) by the time (3 hours), you get the exact distance traveled (162 miles). The incorrect answer of 53 mph does not satisfy this check, as it would only account for 159 miles of travel.

This table provides undeniable proof:

Aspect	Correct Calculation	Incorrect Value
Formula	162 miles / 3 hours	N/A
Result	54 mph	53 mph
Verification	54 * 3 = 162	53 * 3 = 159
Conclusion	Mathematically Correct ✅	Mathematically Incorrect (off by 3 miles) ❌

FAQs About a car left point a at 730 am

What is the difference between speed and velocity?

Speed is a scalar quantity, while velocity is a vector quantity. This means speed only tells you how fast an object is moving (e.g., 54 mph). Velocity, on the other hand, tells you both the speed and the direction of movement (e.g., 54 mph East). Since this problem does not specify a direction, we solve for average speed.

How would the average speed change if the car stopped for 30 minutes?

The average speed would decrease because the total travel time would increase while the distance remains the same. If the car stopped for 30 minutes (0.5 hours), the total journey time would become 3.5 hours. The new average speed would be 162 miles divided by 3.5 hours, which calculates to approximately 46.3 mph.

How do you find the distance if you know the speed and time?

You can rearrange the average speed formula to solve for distance. The new formula is: Distance = Average Speed × Time. For example, if you know a car travels at an average speed of 54 mph for 3 hours, the distance it covers is 54 multiplied by 3, which equals 162 miles.

How do you find the time if you know the speed and distance?

You can also rearrange the formula to solve for time. The equation becomes: Time = Distance / Average Speed. If a car needs to travel 162 miles at an average speed of 54 mph, the time required for the trip is 162 divided by 54, which equals 3 hours.

Does traffic affect the average speed calculation?

Yes, traffic is automatically factored into the average speed. The formula uses the total travel time from the start to the end of the journey. This total time naturally includes any delays caused by slowing down in traffic or stopping at red lights. Average speed reflects the overall pace of the entire trip, not the speed at any single moment.

How do you convert minutes to hours for these problems?

To convert minutes to hours, you divide the number of minutes by 60. For example, 30 minutes becomes 30 ÷ 60 = 0.5 hours. A journey that takes 1 hour and 45 minutes would be calculated as 1 + (45 ÷ 60) = 1.75 hours. This is a critical step for problems where the travel time isn’t a simple whole number.

How can you check your answer in a speed problem?

You can easily check your work by multiplying your calculated speed by the original travel time. The result of this multiplication should equal the total distance given in the problem. In this case, our check is: 54 mph × 3 hours = 162 miles. This matches the problem’s distance, confirming our answer is correct.

Key Takeaways: Solving the “A Car Left Point A” Problem

• The Correct Answer is 54 mph: The final, verified solution is found by dividing the 162-mile distance by the 3-hour travel time.
• The Core Formula is Key: Always start with the standard formula Average Speed = Total Distance / Total Time. Understanding this relationship is the key to solving all uniform motion problems.
• Follow a 3-Step Process: 1) Find total time. 2) Identify total distance. 3) Divide distance by time. This structured approach prevents errors.
• Time Calculation is Crucial: The first step is always to find the total elapsed time. For this problem, the duration from 7:30 AM to 10:30 AM is exactly 3 hours.
• Beware of Common Errors: The incorrect answer of “53 mph” is a calculation mistake. Always verify your division and be wary of distractor answers in tests.

Final Thoughts on Solving Average Speed Problems

Solving a word problem like “a car left point a at 730 am” boils down to a systematic approach rather than complex mathematics. By calmly identifying the key pieces of information—distance and time—and applying the fundamental formula for average speed, you can confidently navigate your way to the correct solution. Remember to always check your units and verify your calculation by working backward. With this clear, three-step method, you are well-equipped to tackle any distance-rate-time challenge that comes your way.