How to Solve Distance Problems Involving Walking and Buses

Understanding distance problems that involve walking and bus travel can be a useful skill in various real-life scenarios. This article will guide you through a typical problem where a student named Raman has to walk part of the way to his school and then take a bus to complete the journey.

Navigating Raman's Journey to School

Let's examine a specific case where Raman’s house is 9/10 km from his school. He walks for a certain distance and then takes a bus for 1/2 km to reach his school. How far did he walk?

Step-by-Step Solution

1. **Total Distance to School**: The total distance from Raman's house to his school is 9/10 km. 2. **Distance Travelled by Bus**: Raman takes a bus to travel 1/2 km, which can also be written as 5/10 km. 3. **Distance Walked by Raman**: To find out the distance Raman walked, we need to subtract the distance he travelled by bus from the total distance to school. This can be calculated as follows:

Distance walked Total distance - Distance travelled by bus Convert the total distance and bus distance to a common denominator (10 in this case):
Total distance 9/10 km Bus distance 5/10 km Subtract the bus distance from the total distance: 9/10 - 5/10 4/10 Simplify the fraction: 4/10 2/5 km

Therefore, Raman walked 2/5 km or 400 meters to reach the bus stop.

Combining Distance Problems

Let's consider another example involving Nandini. The school is 9/10 km away from her house. She takes a bus for 1/2 km to reach her school. How far did she walk?

Solution for Nandini

Total distance to the school: 9/10 km Distance travelled by bus: 1/2 km 5/10 km Distance walked: 9/10 - 5/10 4/10 Simplify the fraction: 4/10 2/5 km

Nandini walked a distance of 2/5 km or 400 meters.

Practical Implications

These types of problems are not just academic exercises; they can be applied in practical situations. For instance, a similar problem can be used to calculate the distance a student walks daily to get to school and back home. Another scenario might involve a person who walks part of the way to work and then takes a bus.

Example with Mira

Mira walks 800 meters one way from her house to the bus stop. So, daily, she walks 1.6 km. She does this because there is no direct bus from her house to the bus stop. This example illustrates that understanding these types of distance problems can help in making informed decisions about travel and commute.

Conclusion

Understanding how to solve distance problems involving walking and bus travel is essential for daily life. By breaking down the problem into manageable steps, such as converting units to a common denominator and then performing the subtraction, these types of problems become straightforward to solve. Whether you are calculating the distance you walk to school, the distance you travel by bus, or the overall distance of a commute, these skills are invaluable.