If you happen to be viewing the article Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race? ? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?
A)
| Activity | Rate (mph) | Time (hours) | Distance (miles) |
|---|---|---|---|
| Run | 8 | t | 8t |
| Bike | 20 | 15 – t | 20(15 – t) |
B)
| Activity | Rate (mph) | Time (hours) | Distance (miles) |
|---|---|---|---|
| Run | 8 | t | 8t |
| Bike | 20 | 1.125 – t | 20(1.125 – t) |
C)
| Activity | Rate (mph) | Time (hours) | Distance (miles) |
|---|---|---|---|
| Run | 1/8 | t | (1/8)t |
| Bike | 1/20 | 1.125 – t | (1/20)(1.125 – t) |
D)
| Activity | Rate (mph) | Time (hours) | Distance (miles) |
|---|---|---|---|
| Run | 1/8 | t | (1/8)t |
| Bike | 1/20 | 15 – t | (1/20)(15 – t) |
Answer:
The correct table that represents Craig’s rates, times, and distances for each part of the race is:
| **A) | Activity | Rate (mph) | Time (hours) | Distance (miles) |
|---|---|---|---|---|
| Run | 8 | t | 8t | |
| Bike | 20 | 1.125 – t | 20(1.125 – t) | ** |
Here’s the explanation for each column:
- Activity: This column specifies the type of activity, either “Run” or “Bike”.
- Rate (mph): This column shows Craig’s average speed in miles per hour for each activity.
- Time (hours): This column represents the time Craig spent on each activity, denoted by ‘t’ for the running time.
- Distance (miles): This column shows the distance covered in each activity. We know the total distance is 15 miles, and it’s the sum of the running and biking distances.
We can use the given information to fill out the table:
- Total distance: 15 miles (given)
- Total time: 1.125 hours (given)
Running:
- We can use the formula distance = rate x time to find the running distance: distance = 8t
- Since the total distance is 15 miles, we can set up an equation: 8t + distance (bike) = 15
Biking:
- We can find the biking time by subtracting the running time from the total time: biking time = total time – running time = 1.125 – t
- The biking distance can be found using the formula distance = rate x time: distance (bike) = 20 (1.125 – t)
Therefore, by filling out the table with the calculated values, we get the answer choice A.
Time and Distance
Time and distance are fundamental concepts in physics and mathematics that describe how objects move through space.
Time: Time is a measurement used to sequence events, to compare the duration of events, and to quantify the intervals between them. In physics, time is often considered as the fourth dimension along with the three spatial dimensions. It is typically measured in units such as seconds, minutes, hours, days, etc.
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Distance: Distance refers to the extent of space between two points or objects. It is a scalar quantity, meaning it has magnitude but no direction. Distance can be measured in various units depending on the context, such as meters, kilometers, miles, etc.
Relationship between Time and Distance: The relationship between time and distance is described by the formula:
Distance = Speed × Time
Where:
- Distance is the extent of space between two points or objects.
- Speed is the rate at which an object covers distance.
- Time is the duration in which the motion occurs.
This formula shows that the distance covered by an object is directly proportional to the speed at which it is moving and the time it travels.
Additionally, if the speed is constant, the relationship between time and distance becomes:
Time = Distance / Speed
This formula can be used to calculate the time taken to cover a certain distance at a constant speed.
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Source: Math Hello Kitty
Categories: Math
