Calculating Train Travel Time at a Constant Speed
Understanding the relationship between distance, speed, and time is crucial for solving real-world problems. This article will walk you through a problem where a train travels 36 km in 21 minutes and asks how long it takes to travel 60 km at the same rate.
Solution 1: Using Speed and Distance Formulas
The first approach involves using the basic formula for speed: Speed (S) Distance (D) / Time (T).
Given: Distance D 36 km and Time T 21 minutes 0.35 hours. First, let's calculate the speed:S 36 ÷ 0.35 102.85 km/hr
Now, we substitute the new distance into our formula to find the time:
T 60 ÷ 102.85 0.58333 hours
Converting 0.58333 hours to minutes:
0.58333 hours 0.58333 × 60 35 minutes
Solution 2: Cross Multiplication Method
A more straightforward method involves cross multiplication, especially useful when dealing with constant speeds. Let's set up our proportion:
Given:
36 km in 0.35 hours 60 km in x hoursSetting up the proportion:
36 km 0.35 hours60 km x hoursx (60 × 0.35) ÷ 36x 21 ÷ 36x 0.58333 hours
Converting 0.58333 hours to minutes:
0.58333 hours 0.58333 × 60 35 minutes
Alternative Method: Unit Conversion Technique
Another approach involves directly converting units to make the calculation easier:
Given: Time taken to cover 36 km 21 minutes Time taken to cover 1 km 21 ÷ 36 minutes Time taken to cover 60 km (21 ÷ 36) × 60 35 minutesBy breaking down the problem into simpler steps, you avoid complications and get a straightforward answer.
Conclusion
Whether you use the speed and distance formula, cross multiplication, or the unit conversion technique, the key is to maintain consistent units and apply the correct method based on the problem's requirements.