Understanding unit rates and how to calculate distances based on speed and time are essential skills in mathematics, with practical applications in everyday life. Whether you’re planning a road trip or solving a real-world math problem, having a solid grasp of these calculations can prove invaluable.
This post breaks down such a problem involving a car travels 284.49 mi in 4.35 hours. We’ll walk you through how to calculate the unit rate (speed) and determine how far the car would travel in 7 hours at that same speed.
What is a Unit Rate?
Before we jump into the specific problem, let’s revisit the concept of a unit rate. A unit rate expresses how much of something occurs in one unit of time, measurement, or quantity. When we talk about speed, the unit rate is commonly represented as miles per hour (mph) or kilometers per hour (km/h).
To calculate a unit rate, divide the total quantity by the total time or units. For example, if someone travels 60 miles in 2 hours, the unit rate is 30 miles per hour (60 ÷ 2 = 30).
Now, with this foundation in mind, let’s tackle our problem.
The Problem
Question:
A car travels 284.49 miles in 4.35 hours.
- What is its unit rate (i.e., speed in miles per hour)?
- If the car maintains this speed, how far will it travel in 7 hours?
By answering these questions step by step, you’ll learn the process of finding unit rates and extrapolating travel distances based on a constant speed.
Step 1: Convert Hours to a Decimal (if necessary)
The total time provided in the question is already in decimal format—4.35 hours. There’s no need for further conversion here. However, it’s good to note this step in case you’re working with time in a different format, like 4 hours and 21 minutes. For example:
- Convert the minutes into a fraction of an hour by dividing the minutes by 60 (e.g., 21 ÷ 60 = 0.35 hours).
- Add the fraction to the whole number of hours (4 hours + 0.35 hours = 4.35 hours).
Step 2: Calculate the Unit Rate (Speed)
To find the unit rate for this car’s travel, divide the total distance by the total time:
Unit rate = Total distance ÷ Total time
- Total distance = 284.49 miles
- Total time = 4.35 hours
Perform the division:
284.49 ÷ 4.35 ≈ 65.4 miles per hour
Thus, the car is traveling at an approximate speed of 65.4 mph
Have you ever wondered how far you can travel if you’re driving at a specific speed for a set amount of time? Questions about speed, distance, and time often arise in real-life scenarios, whether you’re calculating travel times, jogging distances, or understanding how buses and cars work. This blog post breaks it all down with practical examples and easy-to-follow calculations.
By the end of this guide, you’ll be confident in solving these types of problems and understanding fundamental concepts like speed, velocity, and average speed.
How to Calculate Speed, Distance, and Time
The foundation of solving these problems lies in the simple formula for speed:
Speed = Distance ÷ Time
Speed is measured in units like kilometers per hour (km/h), miles per hour (mi/hr), or meters per second (m/s). Once you know how to calculate speed, you can rearrange the formula to solve for distance or time as well. Here’s how it works step by step.
Example 1: A Car Travels 234.40 km in 4 Hours
Let’s start with a simple scenario. If a car travels 234.40 kilometers in 4 hours, how far will it travel in 1 hour?
- Calculate the speed:
Using the formula Speed = Distance ÷ Time, divide 234.40 kilometers by 4 hours.
Speed = 234.40 ÷ 4 = 58.6 km/h
- How far in 1 hour?
Since the car travels at a speed of 58.6 km/h, in 1 hour, it will cover 58.6 kilometers.
Answer: The car travels 58.6 km in 1 hour.
Example 2: Velocity of a Car Traveling 240 Miles South in 3 Hours
Velocity includes not only the speed but also the direction of travel. If a car travels 240 miles south in 3 hours, we can calculate its velocity.
- Calculate velocity in mi/hr:
Velocity = Distance ÷ Time. Divide 240 miles by 3 hours.
Velocity = 240 ÷ 3 = 80 mi/hr south
- Convert to meters/second (m/s):
To convert miles to meters, use the conversion factor 1 mile = 1609.34 meters.
Distance in meters = 240 × 1609.34 = 386,243 meters
Time in seconds = 3 hours × 60 minutes × 60 seconds = 10,800 seconds
Velocity in m/s = 386,243 ÷ 10,800 = 35.76 m/s south
Answer: The velocity of the car is 80 mi/hr south or 35.76 m/s south.
Example 3: A Car Traveling at 40 km/h for 5 Hours
How far does the car travel in this case?
- Apply the formula for distance:
Distance = Time × Speed
Distance = 5 hours × 40 km/h = 200 kilometers
Answer: The car travels 200 kilometers in 5 hours.
Example 4: Calculating Average Speed for a Car Traveling 30 km in 20 Minutes
Average speed is calculated as the total distance divided by the total time taken.
- Convert time to hours:
20 minutes = 20 ÷ 60 = 1/3 hour
- Calculate average speed in km/h:
Average speed = 30 km ÷ 1/3 hour = 90 km/h
Answer: The car’s average speed is 90 km/h.
Example 5: A Bus Travels 350 km in 4 Hours
Now, let’s consider another scenario where a bus travels 350 kilometers in 4 hours. What is its average speed?
- Use the speed formula:
Speed = Distance ÷ Time
Speed = 350 ÷ 4 = 87.5 km/h
Answer: The bus’s average speed is 87.5 km/h.
Example 6: A Person Walking for 2 Hours at 3 m/s
Let’s switch gears to a different kind of motion. How far does a person walk if they travel at a speed of 3 meters per second for 2 hours?
- Convert hours to seconds:
2 hours = 2 × 60 × 60 = 7,200 seconds
- Calculate the distance in meters:
Distance = Speed × Time
Distance = 3 m/s × 7,200 s = 21,600 meters
Answer: The person walks 21,600 meters (or 21.6 kilometers) in 2 hours.
Example 7: Jogging at 10 Meters in 5 Seconds
Lastly, let’s calculate the average speed of a person jogging 10 meters in 5 seconds.
- Use the speed formula:
Speed = Distance ÷ Time
Speed = 10 ÷ 5 = 2 m/s
Answer: The jogger’s average speed is 2 m/s.
Why Understanding Speed and Velocity Matters
Understanding these concepts isn’t just about solving textbook problems—it has real-world applications. Calculating speed, distance, and velocity can help you plan road trips, optimise your travel plans, or even analyze athletic performance. Each calculation shows how motion is measured and understood in everyday scenarios.
Take Action
Now that you’ve got the hang of these calculations, try measuring your own travel speeds or practice with more examples. Whether planning a road trip, training for a marathon, or calculating a commute—these formulas are your ultimate tool.
Feel free to share your favorite use cases for speed and velocity in the comments below, and if you’re still curious, explore more practical math applications on our website.