Time, Speed and Distance for the Assam Police Constable Exam
Time, speed and distance is one of the most reliable chapters of the Elementary Mathematics section in the SLPRB Assam Police Constable (AB & UB) paper. It is built on a single relation, but that relation is applied to so many familiar situations that the chapter can produce a great variety of questions from a small amount of theory. A bus, a train, a boat, a cyclist and a man walking are all handled by the same three quantities and the same three formulas. The reason the chapter is so scoring is that the questions rarely require long calculation; they require the candidate to decide correctly what the distance, the time and the speed are, and then to use the relation in the right direction. Most of the mistakes in this chapter come not from arithmetic but from using inconsistent units, from taking the average of speeds instead of a true average speed, or from mixing up the two directions of relative motion. The method followed here is the one from the Master Book: Maths Masti (D. Hurina), which keeps the three quantities in a small triangle and converts every unit before substituting anything.
Why This Chapter Is Set in Every Assam Police Paper
The topic connects arithmetic with ordinary life, so the examiner can set realistic questions about travel, patrol, transport and streams. It also tests mental discipline: a candidate who writes down what is given and what is asked, and checks the units, will almost always find the answer, while a candidate who substitutes numbers without thinking will fall for the standard traps. Because the same relation answers questions on trains, boats and races, one well-practised idea serves several question types.
Terms You Should Know
- Speed: the distance travelled in unit time.
- Uniform speed: speed that does not change during the journey.
- Average speed: the total distance divided by the total time.
- Relative speed: the speed of one body with respect to another.
- Downstream and upstream: moving with the stream and against it.
- Speed of the stream: the speed of the water current itself.
The base unit in the examination is usually kilometre per hour, but the time given is often in minutes or seconds, so the conversion between kilometre per hour and metre per second must be second nature.
The Running Formula and Its Two Rearrangements
Speed equals distance divided by time, distance equals speed multiplied by time, and time equals distance divided by speed. Every problem in the chapter is a rearrangement of one of these three forms. The safest habit is to write the two given quantities with their units and then look for the third. When two of the three are known, the answer is a single step; when the question hides one quantity behind a condition, the condition is usually there to give that quantity.
Units and the Conversions That Must Be Automatic
To change kilometre per hour into metre per second, multiply by five and divide by eighteen. To change metre per second into kilometre per hour, multiply by eighteen and divide by five. A speed of thirty-six kilometre per hour is ten metre per second, and a speed of fifteen metre per second is fifty-four kilometre per hour. Keep the distance and the time in the same system throughout; a large share of wrong answers in this chapter comes from multiplying a speed in kilometre per hour by a time in minutes without converting one of them.
Average Speed and Why It Is Not the Mean of the Speeds
Average speed is the total distance divided by the total time, and it is not the ordinary mean of the several speeds. For a journey covered in two equal distances at speeds of x and y, the average speed is twice the product of x and y divided by their sum. For a journey covered in equal times at two speeds, the average speed is simply the mean of the two speeds. Deciding whether the distances or the times are equal is the key step, and this is one of the most frequently tested traps in the whole chapter.
Relative Speed and the Two Directions
When two bodies move in opposite directions, their relative speed is the sum of their speeds, so they approach or separate faster. When they move in the same direction, their relative speed is the difference of their speeds. The time taken for a faster body to catch a slower one is the initial distance between them divided by the difference of the speeds. The time taken for two bodies to meet when moving towards each other is the initial distance divided by the sum of the speeds. Writing "same direction subtract, opposite direction add" at the top of the rough sheet prevents a whole class of errors.
Problems on Trains
A train passing a pole or a standing man covers only its own length, but a train passing a platform, a bridge or another train covers its own length together with the length of the other object. When two trains cross each other, their relative speed is the sum for opposite directions and the difference for the same direction, and the total distance is the sum of their lengths. Questions on how long a train takes to pass a signal, a bridge or another moving train are among the most common in the paper, and all of them follow from these two ideas.
Boats and Streams
The speed of a boat downstream is the speed of the boat in still water plus the speed of the stream, and the speed upstream is the speed of the boat in still water minus the speed of the stream. From these two, the speed in still water is the average of the downstream and upstream speeds, and the speed of the stream is half the difference of the two. Questions on the total time for a round trip are solved by writing the time downstream and the time upstream separately and adding them. When the boat has to travel the same distance up and down, the average speed is found from the reciprocal method rather than by taking the arithmetic mean.
Shortcut Techniques for the Exam Hall
Convert the speed to metre per second at once if the answer is to be in seconds. For a train, decide at the start whether the distance is the train alone or the train plus the object. For average speed over equal distances, use the product over sum form. For relative motion, write the word "add" or "subtract" before any calculation. For boats, find the two speeds first and then form the sum and the difference, since almost every question asks for one of these combinations.
Common Traps and Errors
- Using a speed in kilometre per hour with a time in minutes or seconds.
- Taking the mean of the speeds instead of the total distance divided by the total time.
- Forgetting to include the length of the platform or the other train in a crossing problem.
- Adding the speeds when two trains move in the same direction, or subtracting when they move in opposite directions.
- Confusing the speed of the stream with the speed of the boat in still water.
- Applying the equal-distance average speed formula when the times, and not the distances, are equal.
A Study Plan for This Chapter
- Make the three forms of the speed formula automatic.
- Practise the two unit conversions until they need no thought.
- Work on average speed for equal distances and for equal times separately.
- Practise relative speed, trains and boats and streams as three groups.
- Finish with a mixed set and always write the units before substituting.
Frequently Asked Questions
How do I change kilometre per hour into metre per second?
Multiply by five and divide by eighteen. For example, thirty-six kilometre per hour becomes thirty-six times five divided by eighteen, which is ten metre per second.
Why can I not simply average the two speeds of a journey?
Because the two speeds were used for different lengths of time or different distances. Average speed is the total distance divided by the total time, and only when the times are equal does it equal the ordinary mean of the speeds.
What is the relative speed of two trains moving in opposite directions?
The relative speed is the sum of the two speeds. When the trains move in the same direction, the relative speed is the difference of the two speeds.
How much distance does a train cover while passing a platform?
It covers its own length plus the length of the platform. While passing a pole or a standing man, it covers only its own length.
How do I find the speed of a boat in still water and the speed of the stream?
The speed in still water is the average of the downstream and upstream speeds, and the speed of the stream is half their difference. The downstream speed is the boat in still water plus the stream, and the upstream speed is the boat minus the stream.