Calculating Distance to School Using Speed and Time
Have you ever wondered how to calculate the distance to your school based on your walking or cycling speed and the time you are early or late? Let's explore how to solve such problems step by step. This guide will walk you through the process using various examples.
Example 1: Walking to School at Different Speeds
A student walks from his house at 2.5 km/hr and reaches his school late by 6 minutes. Next day, he increases his speed to 3.5 km/hr and reaches 6 minutes before school time. How far is the school from his house?
Let D denote the required distance in km of the school from his house.
Hence from the above data, we get the following relation:
D/2.5 - D/3.5 1/5
Further simplifying, we find:
2D - 10D/7 1 4D/7 1 D 7/4 1.75 kmAnswer: The school is 1.75 km from the student's house.
Example 2: Using Simple Algebraic Equations to Solve
Let the distance be x km. The difference in time taken for the two speeds is 6 minutes.
x/2.5 - x/3.5 6/60 1/4
Simplifying further:
5x - 4x 5 x 5 kmAnswer: The school is 5 km from the student's house.
Example 3: A More Challenging Example with Time Difference
A student rides on a bicycle at 8 km/h and reaches his school 2.5 minutes late. The next day, he increases his speed to 10 km/h and reaches the school 5 minutes early. How far is the school from his house?
Let the distance covered by the student be D km, and the normal time T hours.
D/8 T 2.5/60 …1
D/10 T - 5/60 …2
Subtracting equation 2 from equation 1:
(D/8) - (D/10) (T 2.5/60) - (T - 5/60)
D/8 - D/10 2.5/60 5/60
(5D - 4D) / 40 7.5 / 60
D 7.5 * 40 / 60 5 km
Answer: The distance from home to the school is 5 km.
Conclusion
Understanding how to calculate distance based on speed and time can be quite useful in real-life scenarios. Whether you are walking, cycling, or even driving, this knowledge helps in planning and managing your time effectively.