Tips and Tricks for Speed, Distance and Time

Speed, Time, and Distance questions are foundational in quantitative aptitude exams, often determining time management and problem-solving speed.

This topic is crucial because it tests mathematical skills and evaluates a candidate’s logical thinking and ability to apply formulas effectively under pressure.

Key Formulas for Speed, Distance, and Time

Basic Formulas for Speed, Distance, and Time:

• Speed = Distance / Time
• Distance = Speed × Time
• Time = Distance / Speed

These formulas can be remembered using a simple acronym DST where D stands for Distance, S for Speed, and T for Time, and can be visualized as below:

Unit Conversion Tips

Here is a table to convert various units.

Shortcut Tricks for Speed Distance and Time Questions

Average Speed for Varying Distances

Formula:

Average Speed = Total Distance/Total Time

When to Use: This formula is helpful when a journey consists of different distances covered at different speeds.

Average Speed for Equal Distances at Different Speeds

Formula:

Average Speed = (2 × Speed 1 × Speed 2)/(Speed 1 + Speed 2)

When to Use: Use this formula when covering equal distances at two different speeds, such as going to a location at one speed and returning at another.

Relative Speed

Relative speed helps understand the effective speed between two moving objects, useful for solving problems involving trains, cars, or boats.

• Same Direction:
  • Relative Speed = Difference of Speeds
    • Example: Two trains moving at 80 km/h and 60 km/h in the same direction:
    • Relative Speed = 80 - 60 = 20 km/h
• Opposite Directions:
  • Relative Speed = Sum of Speeds
    • Example: Two trains moving at 80 km/h and 60 km/h toward each other:
    • Relative Speed = 80 + 60 = 140 km/h

Time to Meet or Overtake

• Meeting Time:
  • Time = Distance ÷ Relative Speed
  • Example: Two cars 300 km apart moving toward each other at 50 km/h and 70 km/h:
    • Relative Speed = 50 + 70 = 120 km/h
    • Time = 300 ÷ 120 = 2.5 hours
• Overtaking Time:
  • Time = Distance ÷ Relative Speed
  • Example: A faster car overtaking a slower car 100 meters ahead, with speeds of 20 m/s and 15 m/s respectively:
    • Relative Speed = 20 - 15 = 5 m/s
    • Time = 100 ÷ 5 = 20 seconds

Train Problems

Passing a Stationary Object: When a train passes a stationary object, the distance covered is equal to the length of the train.

Formula: Time = Length of Train ÷ Speed

Example: A train 275 meters long is moving at a speed of 66 km/h. How long will it take for the train to pass a stationary signal post?

Length of Train = 275 meters

Speed = 68 km/h

• Convert speed to meters per second:
  • Speed = 68 × (5/18) ≈ 18.89 m/s
• Time = Length of Train ÷ Speed
  • 275 ÷ 18.89 ≈ 14. 56 seconds

The train will take approximately 14.56 seconds to pass the stationary signal post completely.

Train Passing a Platform: When a train passes a platform, the distance covered is the sum of the lengths of the train and the platform.

Formula: Time = (Length of Train + Length of Platform) ÷ Speed

Example: A train 225 meters long is traveling at a speed of 60 km/h. How long will it take for the train to completely pass a platform that is 180 meters long?

Length of Train = 225 meters

Length of Platform = 180 meters

Speed = 60km/h

• Convert Speed to Meters per Second:
  • Speed = 60 × (5/18) = 16.67 m
• Calculate Total Distance to Pass the Platform:
  • Total Distance = Length of Train + Length of Platform
  • Total Distance = 225 meters + 180 meters = 405 meters
• Calculate Time to Pass the Platform:
  • Time = Total Distance ÷ Speed
  • Time = 405 meters ÷ 16.67 m/s ≈ 24.3 seconds

The train will take approximately 24.3 seconds to pass the stationary signal post completely.

Related Reads:

• Speed, Time, and Distance.
• Practice Quiz on Speed Time and Distance.
• Problem on Time Speed and Distance