Calculating Distance: A Journey of 30 minutes at 7/2 km/h

Imagine a young boy traveling to school for 30 minutes at a steady pace of 7/2 km/h. How can we determine how far he travels, given his speed and the time he takes? This article will guide you through the steps to solve such a problem using a combination of basic algebra and physics. We will use different methods to arrive at the same answer, ensuring a comprehensive understanding of the underlying concepts.

Method 1: Direct Calculation Using Speed and Time

The fundamental formula to calculate distance in physics is:

Distance Speed times; Time

Here are the steps to solve the problem using this formula:

Convert the speed from km/h to km/min. Express the time in a consistent unit (min or hr). Calculate the distance.

Step-by-Step Solution

The boy's speed is given as 7/2 km/h. To convert this to km/min:

SPEED (7/2) times; (1/60) 7/120 km/min

The problem states that the boy takes 30 minutes to reach his school. Using the distance formula:

DISTANCE (7/120) times; 30 70/120 7/12 km 1.75 km

Therefore, the school is 1.75 km from the boy's house.

Method 2: Algebraic Solution

Let's explore a different approach using algebraic equations. Assume the distance to the school is x km.

T1 x / (7/2) 2x/7 (in hours)

T2 x / (5/4) 4x/5 (in hours)

Subtract the times: (4x/5) - (2x/7) 15/60 1/4 (in hours)

Converting to a common denominator:

(28x - 1) / 35 1/4

18x 35/4

x 35/72 km

This method is complex and involves solving algebraic equations, but we can simplify it by recognizing common times and speeds.

Additional Solutions

Other methods to solve the problem include:

1.75 km (as calculated in Step 1). 5 km (as derived from solving the equation). 5 km, using unit conversion and time differences.

Each method ultimately leads to the same conclusion: the school is 5 km from the boy's house.

Conclusion

The distance from the boy's house to his school is 5 km, regardless of the method used. Understanding and applying basic physics principles can provide clarity and ensure accurate solutions to real-world problems. Whether using direct calculations, algebraic equations, or unit conversion, the key is to maintain consistency in units and carefully follow each step to reach the correct answer.