Student’s Walking Speed and Distance Calculations
Have you ever wondered how distance, speed, and time interrelate in real-life scenarios, such as a student’s commute to school? This article explores a practical problem to understand how these concepts work and provides a step-by-step solution. By the end, you will have a clearer understanding of how to approach similar problems.
The Problem
A student walks from their house to school. On the first day, the student walks at a speed of 2 km/hr and reaches school 2 minutes late. Next day, the student increases their speed to 3 km/hr and arrives 6 minutes early. The problem requires us to find the distance from the student's house to the school.
The Solution
Symbolic Representation
Let's denote the distance from the student's house to the school as d kilometers.
Formulating the Equations
Given the information, we can form two key equations based on the relationship between distance, speed, and time. The time taken to travel a distance can be expressed as:
Time Distance / Speed
First Day: Speed 2 km/hr, student is 2 minutes late.
Let t represent the time it takes to reach school on time (in hours).
The time taken on the first day is:
Time_1 d / 2
Since the student is 2 minutes late, we convert this to hours:
2 minutes 2/60 1/30 hours
Thus, the equation becomes:
d / 2 t 1/30
d / 2 - t 1/30(1)
Second Day: Speed 3 km/hr, student is 6 minutes early.
The time taken on the second day is:
Time_2 d / 3
Since the student arrives 6 minutes early, we convert this to hours:
6 minutes 6/60 1/10 hours
Thus, the equation becomes:
d / 3 t - 1/10
d / 3 - t -1/10(2)
Solving the Equations
We can solve these two equations to find d and t.
From equation (1):
t d / 2 - 1/30
From equation (2):
t d / 3 - 1/10
Equating the two expressions for t:
d / 2 - 1/30 d / 3 - 1/10
Clearing the fractions by multiplying through by 30:
15d - 1 10d - 3
5d 2
d 2/5
d 0.4 kilometers
Conclusion
The distance from the student's house to the school is 0.4 kilometers (or 400 meters).
Key Concepts to Remember
Distance Speed × Time
Time Distance / Speed
This problem demonstrates the practical application of these concepts and helps in solving real-life scenarios involving distance and speed.
Practical Tips
- Always convert all given time measurements to the same unit (hours in this case).
- Use symbols for unknown values to formulate equations.
- Equate expressions for the same variable (in this case, t) to solve the problem.
Conclusion Summary
The distance from the student's house to the school is 0.4 kilometers, which can also be expressed as 400 meters. This solution has been verified by solving two simultaneous equations based on the given conditions.