RRB ALP Maths Time Speed And Distance, Check Important Formulas with Examples

Time, Speed, and Distance is one of the most important topics in the RRB ALP Maths section. Many questions in the exam are based on simple concepts like relative speed, average speed, stoppage time, trains, and meeting point problems. If students understand the basic formulas and practise enough questions, this topic can become scoring.

In the RRB ALP Maths Time Speed and Distance topic, students should focus on concept clarity and quick calculation. Questions may look lengthy, but most of them can be solved easily by applying the right formula. 

Also Read: 

• RRB ALP Syllabus
• RRB ALP Previous Year Question Papers

Time, Speed and Distance Basic Formula

The basic formula of Time, Speed and Distance is very simple:

Distance = Speed × Time

From this formula, we can also write:

• Speed = Distance / Time

• Time = Distance / Speed

Students should also remember unit conversion. If speed is given in km/h and time is given in minutes, convert minutes into hours before solving.

For example, 30 minutes = 1/2 hour and 45 minutes = 3/4 hour.

Relative Speed in Time, Speed, and Distance

Relative speed is used when two objects are moving together. It helps us find how fast the distance between them is changing.

Important points:

• If two objects move towards each other, their speeds are added.

• If two objects move in the same direction, their speeds are subtracted.

• Relative speed is very useful in train and meeting point questions.

For example, if two trains start from two points 180 km apart and meet after 3 hours, their combined speed will be 180/3 = 60 km/h. If one train’s speed is 35 km/h, the other train’s speed will be 25 km/h.

Stoppage Time Per Hour Formula

Stoppage time questions are common in competitive exams. These questions are based on the difference between speed without stoppage and speed with stoppage.

The formula is:

Stoppage Time per Hour = [(Speed without stoppage - Speed with stoppage) / Speed without stoppage] × 60

For example, if a bus travels at 60 km/h without stoppage and 54 km/h with stoppage, then:

Stoppage time = [(60 - 54) / 60] × 60 = 6 minutes

So, the bus stops for 6 minutes per hour.

Average Speed in Round Trip Questions

Average speed questions become slightly tricky when the object covers the same distance at two different speeds. In such cases, do not take the simple average. If a person goes at speed S1 and returns the same distance at speed S2, then:

Average Speed = (2 × S1 × S2) / (S1 + S2)

For example, if a delivery boy goes at 32 km/h and returns at 24 km/h, the average speed will be:

Average Speed = (2 × 32 × 24) / (32 + 24)

This formula is useful when the same distance is covered twice at different speeds. Students should practise this type because it saves a lot of time in the exam.

Train Accident Problems in Time Speed and Distance

Train accident questions are important for RRB ALP Maths. These questions are usually based on reduced speed after an accident and delay in reaching the destination. The key concept is that speed and time are inversely related when distance is constant.

If speed decreases, time increases. For example, if a train runs at 2/3 of its original speed, then the time ratio becomes 3:2.

Important steps to solve these questions:

• Find the changed speed ratio.

• Convert it into a time ratio.

• Use the delay to find normal time.

• Compare two given cases if the accident point changes.

• Find original speed using distance/time.

• Finally, calculate the total distance.

For example, if a train has an accident after 120 km and then travels at 2/3 of its original speed, the delay can be used to find the remaining journey time. If another case is given where the accident happens 60 km further, the difference in normal time helps calculate the original speed.

Meeting Point with Return Journey

Meeting point questions are also important in the Time, Speed and Distance chapter. In this type of question, two people start from the same point or opposite points. One person reaches the destination first, turns back, and meets the slower person.

Steps to solve these questions:

• Find the time taken by the faster person to reach the destination.

• Calculate the distance covered by the slower person in that time.

• Find the remaining distance between them.

• Use relative speed to find the meeting time.

• Calculate the meeting point distance.

For example, if two people start from A to B, and the faster person reaches B first and returns immediately, the meeting point can be found using relative speed. Since they are now moving towards each other, their speeds will be added.

Train Meeting Problems After Encounter

This is a special and very useful type of train question. In this type, two trains start from opposite stations and move towards each other. After meeting, they continue their journey and take different times to reach their destinations.

Important formula:

Time taken to meet = √(t1 × t2)

Here, t1 and t2 are the times taken by the two trains after meeting to reach their destinations.

Another useful formula is:

Speed ratio = √(t2/t1)

For example, if train X takes 9 hours after meeting and train Y takes 16 hours after meeting, then:

Time taken to meet = √(9 × 16)
= √144
= 12 hours

So, both trains met after 12 hours. The slower train will take more total time to complete the journey.

Important RRB ALP TSD Formulas

Students should revise these formulas regularly:

• Distance = Speed × Time

• Speed = Distance / Time

• Time = Distance / Speed

• Relative speed when moving towards each other = S1 + S2

• Relative speed in the same direction = S1 - S2

• Average speed for round trip = (2 × S1 × S2) / (S1 + S2)

• Stoppage time per hour = Speed loss ratio × 60

• Meeting time after encounter = √(t1 × t2)

Preparation Tips for RRB ALP Time Speed and Distance Topic

To score well in this topic, students should focus on both accuracy and speed. First, understand the basic formula and then practise different types of questions. Students should follow these tips:

• Practise relative speed questions daily.

• Revise stoppage time formula properly.

• Solve train questions step by step.

• Learn average speed formulas for round trips.

• Attempt previous year questions.

• Re-solve class examples without seeing the solution.

• Focus on one-line solution methods after learning the concept.

Speed improves only with repetition. Students should practise the same question types multiple times until the method becomes clear.