Calculating Time and Distance at Different Speeds: A Comprehensive Guide

When dealing with transportation and logistics, understanding how to calculate the time and distance at different speeds is crucial. This article will walk you through the process of determining the time it takes for a bus to travel a certain distance at various speeds. By using examples and formulas, we aim to provide a clear understanding of the underlying principles.

Understanding the Relationship Between Speed, Distance, and Time

The formula relating speed, distance, and time is fundamental in solving such problems. The formula is:

Distance Speed × Time Time Distance ÷ Speed Speed Distance ÷ Time

With this formula, you can easily manipulate the equation to find any of the three variables, given the other two.

Problem 1: Calculating Time with a Given Speed and Distance

Consider a bus that covers a certain distance in 3 hours and 20 minutes at an average speed of 45 km per hour. To find out how much time it will take to cover the same distance at a speed of 50 km per hour, follow these steps:

Step 1: Convert Time to Hours

The time taken is 3 hours and 20 minutes. To convert this into hours, perform the following calculation:

$$3 text{ hours} frac{20 text{ minutes}}{60} 3 frac{1}{3} frac{10}{3} text{ hours} $$

Step 2: Calculate the Distance

Using the formula for distance:

$$text{Distance} text{Speed} times text{Time} $$

Substituting the values:

$$text{Distance} 45 text{ km/h} times frac{10}{3} text{ hours} 150 text{ km} $$

Step 3: Calculate the Time to Cover the Same Distance at 50 km/h

Using the formula for time:

$$text{Time} frac{text{Distance}}{text{Speed}} $$

Substituting the values:

$$text{Time} frac{150 text{ km}}{50 text{ km/h}} 3 text{ hours} $$

Therefore, it will take 3 hours to cover the same distance at a speed of 50 km per hour.

Conclusion: The time required to cover the distance at 50 km/h is 3 hours.

Additional Examples

Example 1: Multiple Speeds

For a bus that covers a distance of 150 km at 45 km/h at one speed, and the same distance at 36 km/h, calculate the time taken.

Distance 150 km

Speed 36 km/h

Time required to travel 150 km at 36 km/h:

$$text{Time} frac{150 text{ km}}{36 text{ km/h}} 4.166 text{ hours} ≈ 4 hours 10 minutes.$$

Example 2: Different Speeds

If a bus travels 42 km at 45 km/h for 3 hours, then at 36 km/h, the time taken is:

Distance 42×10/3 150 km

Speed 36 km/h

Time 150/36 4.166 hours ≈ 4 hours 10 minutes.

Summary and Conclusion

Understanding the relationship between speed, distance, and time is essential for solving real-world problems in logistics and transportation. By using the fundamental formulas, you can easily calculate the time required to cover a certain distance at different speeds.

Conclusion: The time required to cover 150 km at 50 km/h is 3 hours. The time required to cover the same distance at 36 km/h is approximately 4 hours 10 minutes.