Introduction
This chapter is dedicated to a critical theme in the quantitative aptitude portion of various competitive examinations: Time and Distance. This topic revolves around calculations involving time, distance, and speed, and their interrelation. A basic understanding of algebra and units of measurement is crucial to mastering this topic.
Importance in SSC, RRB, and Banking Exams
Questions on Time and Distance are common in competitive examinations such as the Staff Selection Commission (SSC), Railway Recruitment Board (RRB), and various Banking Exams. These problems test a candidate’s quantitative skills, conversion ability, and problem-solving skills. Often these problems also incorporate concepts of ratio and proportion, making them a key aspect of the Quantitative Aptitude section.
Basic Formulas and Concepts
The three fundamental concepts in this topic are Time, Distance, and Speed, and they are interrelated by the formula:
Distance = Speed x Time
Here are some other important concepts related to Time and Distance:
- Relative Speed: The relative speed of two bodies moving in the same or opposite directions is the sum or difference of their speeds, respectively.
- Average Speed: Average speed is total distance divided by total time taken.
Advanced Concepts and Problem Types
Some of the advanced concepts and types of problems you will encounter related to Time and Distance are:
- Train Problems: These problems typically involve calculations of time and distance involving moving trains and often require the concept of relative speed.
- Boats and Streams: These problems involve calculating the speed of a boat in still water and the speed of the stream to determine the downstream and upstream speeds.
- Races and Games of Skill: These problems involve analyzing races between two or more participants, taking into account their relative speeds and the concept of start advantage or handicap.
Problem-Solving Techniques and Examples
Let’s discuss a few types of problems and how to solve them:
Basic Time and Distance Problems
Example: If a car travels at a speed of 60 km/h, how long will it take to cover a distance of 240 km?
Here, we can use the basic formula. Time = Distance / Speed. So, the time taken is 240 / 60 = 4 hours.
Train Problems
Example: Two trains, each 100 m long, are running in opposite directions. They cross each other in 8 seconds. If one is running twice as fast as the other, find their speeds.
Let the speed of the slower train be ‘x’ m/s. Then the speed of the faster train is ‘2x’ m/s. The total distance to be covered is the sum of the lengths of the two trains, which is 100 + 100 = 200 m. They cross each other in 8 seconds. So, 200 = (x + 2x) * 8. Solving this equation gives x = 25/3 m/s, which is approximately 30 km/h. Hence, the speeds of the trains are 30 km/h and 60 km/h.
Practice Problems
To hone your time and distance skills, try to solve the following problems:
- A man takes 5 hours 45 minutes in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. How long would he take to walk both ways?
- Two men start walking towards each other at the same time from points A and B, which are 72 km apart. They meet 6 hours after starting. If they had walked in the same direction, they would have met after 9 hours. Find their speeds.
- A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 460 m long?
Summary
Time and Distance problems require a firm understanding of speed, time, and distance, and their relationship. Understanding the concepts of relative speed and average speed is crucial. An analytical approach, combined with the ability to formulate and solve equations, is important to solve these problems efficiently. Remember to carefully read the problem and draw diagrams if necessary to visualize the problem.