Calculating Time to Cover 280 km

Oct 13, 2025 by leolavanderia.com.br 42 views

Calculating Train Speed and Time

When it comes to calculating the speed of a train or any other vehicle, we need to consider the distance it covers and the time it takes to cover that distance. In this article, we will explore how to calculate the speed of a train and use it to determine the time it would take to cover a certain distance.

Calculating Train Speed

To calculate the speed of a train, we can use the formula:

Speed = Distance / Time

In this case, the train covers a distance of 120 km in 1 hour and 30 minutes. We need to convert the time from hours and minutes to just hours. There are 60 minutes in an hour, so 30 minutes is equal to 0.5 hours. Therefore, the total time taken by the train to cover 120 km is 1.5 hours.

Now, we can calculate the speed of the train using the formula:

Speed = 120 km / 1.5 hours Speed = 80 km/h

Calculating Time to Cover 280 km

Now that we know the speed of the train, we can use it to calculate the time it would take to cover 280 km. We can use the formula:

Time = Distance / Speed

Plugging in the values, we get:

Time = 280 km / 80 km/h Time = 3.5 hours

Therefore, the train would take 3.5 hours to cover 280 km.

Understanding Ratios and Equivalent Ratios

Now, let's move on to the second part of the problem, which involves understanding ratios and equivalent ratios. A ratio is a comparison of two numbers or quantities. Equivalent ratios are ratios that have the same value, but may be expressed in different ways.

Understanding Equivalent Ratios

To determine if two ratios are equivalent, we need to check if they have the same value. We can do this by cross-multiplying the ratios and checking if the resulting products are equal.

For example, let's consider the two ratios:

Ratio 1: 2:3 Ratio 2: 4:6

To check if these ratios are equivalent, we can cross-multiply them:

2 x 6 = 12 3 x 4 = 12

Since the resulting products are equal, we can conclude that the two ratios are equivalent.

Are the Two Ratios Equivalent?

Now, let's apply this concept to the two ratios given in the problem:

Ratio 1: 120:180 Ratio 2: 65:130

To check if these ratios are equivalent, we can cross-multiply them:

120 x 130 = 15600 180 x 65 = 11700

Since the resulting products are not equal, we can conclude that the two ratios are not equivalent.

Conclusion

In conclusion, we have learned how to calculate the speed of a train and use it to determine the time it would take to cover a certain distance. We have also learned how to understand ratios and equivalent ratios, and how to apply this concept to determine if two ratios are equivalent.

Key Takeaways

To calculate the speed of a train, we can use the formula: Speed = Distance / Time
To calculate the time it would take to cover a certain distance, we can use the formula: Time = Distance / Speed
Equivalent ratios are ratios that have the same value, but may be expressed in different ways.
To determine if two ratios are equivalent, we can cross-multiply them and check if the resulting products are equal.

Final Answer

The final answer to the problem is:

The train would take 3.5 hours to cover 280 km.
The two ratios are not equivalent.
Frequently Asked Questions (FAQs) =====================================

Q: What is the formula to calculate the speed of a train?

A: The formula to calculate the speed of a train is:

Speed = Distance / Time

Q: How do I convert time from hours and minutes to just hours?

A: To convert time from hours and minutes to just hours, you can divide the number of minutes by 60. For example, if the time is 1 hour and 30 minutes, you can convert it to just hours by dividing 30 by 60, which equals 0.5 hours. Therefore, the total time taken by the train to cover 120 km is 1.5 hours.

Q: How do I calculate the time it would take to cover a certain distance?

A: To calculate the time it would take to cover a certain distance, you can use the formula:

Time = Distance / Speed

Q: What is the difference between a ratio and an equivalent ratio?

A: A ratio is a comparison of two numbers or quantities. An equivalent ratio is a ratio that has the same value, but may be expressed in different ways.

Q: How do I determine if two ratios are equivalent?

A: To determine if two ratios are equivalent, you can cross-multiply them and check if the resulting products are equal.

Q: What is cross-multiplication?

A: Cross-multiplication is a method of multiplying two ratios by multiplying the corresponding terms. For example, if we have two ratios:

Ratio 1: 2:3 Ratio 2: 4:6

We can cross-multiply them by multiplying 2 and 6, and 3 and 4, which gives us:

2 x 6 = 12 3 x 4 = 12

Since the resulting products are equal, we can conclude that the two ratios are equivalent.

Q: Can you give an example of equivalent ratios?

A: Yes, here are two equivalent ratios:

Ratio 1: 2:3 Ratio 2: 4:6

As we can see, the two ratios have the same value, but are expressed in different ways.

Q: Can you give an example of non-equivalent ratios?

A: Yes, here are two non-equivalent ratios:

Ratio 1: 2:3 Ratio 2: 4:5

As we can see, the two ratios do not have the same value, and are therefore not equivalent.

Q: How do I apply the concept of equivalent ratios to real-life situations?

A: The concept of equivalent ratios can be applied to many real-life situations, such as:

Comparing the prices of different products
Comparing the weights of different objects
Comparing the speeds of different vehicles

By understanding equivalent ratios, you can make more informed decisions and solve problems more efficiently.

Q: What are some common mistakes to avoid when working with ratios?

A: Some common mistakes to avoid when working with ratios include:

Not converting the ratios to equivalent forms
Not cross-multiplying the ratios
Not checking if the resulting products are equal

By avoiding these mistakes, you can ensure that your calculations are accurate and reliable.

Q: Can you provide more examples of equivalent ratios?

A: Yes, here are some more examples of equivalent ratios:

1:2 = 2:4
3:5 = 6:10
2:3 = 4:6

As you can see, the equivalent ratios have the same value, but are expressed in different ways.