transportation engineering

Oct 13, 2025 by miodeya.com 125 views

Understanding the Problem

To solve this problem, we need to understand the relationship between the distance Phumzile cycles and the time it takes her to cycle that distance. Phumzile's cycling speed is a crucial factor in determining how far she can cycle in a given time. In this case, we are given that she can cycle 5km in 10 minutes.

Calculating Phumzile's Cycling Speed

To calculate Phumzile's cycling speed, we need to divide the distance she cycles (5km) by the time it takes her to cycle that distance (10 minutes). This will give us her speed in kilometers per minute.

Speed = Distance / Time
Speed = 5 km / 10 minutes
Speed = 0.5 km/minute

Applying the Concept of Proportionality

Now that we know Phumzile's cycling speed, we can use the concept of proportionality to determine how far she can cycle in 7 minutes. Proportionality is a mathematical concept that states that if two quantities are proportional, then the ratio of the two quantities remains constant.

In this case, we can set up a proportion to relate the distance Phumzile cycles in 10 minutes (5km) to the distance she cycles in 7 minutes (x km).

5 km / 10 minutes = x km / 7 minutes

Solving for x

To solve for x, we can cross-multiply the proportion and then divide both sides by 7 minutes.

5 km * 7 minutes = 10 minutes * x km
35 km * minutes = 10x km * minutes
35 = 10x
x = 35 / 10
x = 3.5 km

Conclusion

Therefore, if Phumzile cycles 5km in 10 minutes, she can cycle 3.5km in 7 minutes.

Real-World Applications

This problem may seem trivial, but it has real-world applications in fields such as transportation engineering, where understanding the relationship between distance and time is crucial in designing efficient transportation systems.

Tips and Tricks

When solving problems involving proportionality, make sure to set up the proportion correctly and then solve for the unknown variable.
Use the concept of proportionality to relate different quantities and solve problems involving ratios and proportions.

Common Mistakes

Failing to set up the proportion correctly
Not solving for the unknown variable
Not using the concept of proportionality to relate different quantities

Additional Resources

Khan Academy: Proportionality
Math Is Fun: Proportion
Wolfram Alpha: Proportionality

Final Thoughts

In conclusion, if Phumzile cycles 5km in 10 minutes, she can cycle 3.5km in 7 minutes. This problem demonstrates the importance of understanding the concept of proportionality and how it can be applied to real-world problems. By following the steps outlined in this article, you can solve similar problems and develop a deeper understanding of mathematical concepts.

Frequently Asked Questions

Q: What is the relationship between distance and time in this problem?

A: The relationship between distance and time is one of proportionality. This means that if Phumzile cycles 5km in 10 minutes, she will cycle a certain distance in 7 minutes that is proportional to the distance she cycles in 10 minutes.

Q: How do I calculate Phumzile's cycling speed?

A: To calculate Phumzile's cycling speed, you need to divide the distance she cycles (5km) by the time it takes her to cycle that distance (10 minutes). This will give you her speed in kilometers per minute.

Q: What is the formula for calculating Phumzile's cycling speed?

A: The formula for calculating Phumzile's cycling speed is:

Speed = Distance / Time

Q: How do I apply the concept of proportionality to solve this problem?

A: To apply the concept of proportionality, you need to set up a proportion to relate the distance Phumzile cycles in 10 minutes (5km) to the distance she cycles in 7 minutes (x km). Then, you can solve for x using the proportion.

Q: What is the proportion that I need to set up to solve this problem?

A: The proportion that you need to set up is:

5 km / 10 minutes = x km / 7 minutes

Q: How do I solve for x in the proportion?

A: To solve for x, you can cross-multiply the proportion and then divide both sides by 7 minutes.

Q: What is the value of x in the proportion?

A: The value of x in the proportion is 3.5 km.

Q: What is the real-world application of this problem?

A: The real-world application of this problem is in fields such as transportation engineering, where understanding the relationship between distance and time is crucial in designing efficient transportation systems.

Q: What are some common mistakes that people make when solving this problem?

A: Some common mistakes that people make when solving this problem include failing to set up the proportion correctly, not solving for the unknown variable, and not using the concept of proportionality to relate different quantities.

Q: Where can I find additional resources to help me understand this problem?

A: You can find additional resources to help you understand this problem on websites such as Khan Academy, Math Is Fun, and Wolfram Alpha.

Additional Q&A

Q: What if Phumzile cycles 10km in 20 minutes? How many kilometres does she cycle in 14 minutes?

A: To solve this problem, you need to calculate Phumzile's cycling speed using the formula Speed = Distance / Time. Then, you can use the concept of proportionality to set up a proportion and solve for the unknown variable.

Q: What if Phumzile cycles 15km in 30 minutes? How many kilometres does she cycle in 21 minutes?

Conclusion

In conclusion, the problem of Phumzile cycling 5km in 10 minutes and then cycling a certain distance in 7 minutes is a classic example of a proportionality problem. By understanding the concept of proportionality and applying it to the problem, you can solve for the unknown variable and gain a deeper understanding of mathematical concepts.

Final Thoughts

We hope that this Q&A article has helped you to understand the problem of Phumzile cycling 5km in 10 minutes and then cycling a certain distance in 7 minutes. If you have any further questions or need additional help, please don't hesitate to ask.