Speed Time and Distance: Formulas, Tricks and Examples

Speed Time and Distance questions use the relationship between distance travelled, time taken and speed. This page covers the basic speed time distance formula, unit conversions, average speed, relative speed, trains, boats and common TSD shortcuts with clear numerical examples.

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What is Speed, Time and Distance?

Speed is the distance covered per unit of time. The three quantities are related by the formula: Distance = Speed × Time.

The main speed time distance formulae are Speed = Distance ÷ Time and Time = Distance ÷ Speed. If speed is measured in kilometres per hour and time in hours, distance is obtained in kilometres. For example, a car travelling at 60 km/h for 2 hours covers 60 × 2 = 120 km.

Speed Time and Distance Formula & Tricks

Important Formulas

Basic distance formula
Distance = Speed × Time

Use this when speed and time are known. The units of speed and time must be compatible.

Speed formula
Speed = Distance ÷ Time

Speed is the distance travelled divided by the time taken.

Time formula
Time = Distance ÷ Speed

Time is found by dividing distance by speed.

Unit conversion
1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h

Multiply km/h by 5/18 to convert it into m/s. Multiply m/s by 18/5 to convert it into km/h.

Average speed
Average speed = Total distance ÷ Total time

Average speed is not generally the arithmetic mean of the individual speeds.

Relative speed
Same direction: |u − v|; Opposite directions: u + v

Relative speed gives the rate at which the distance between two moving objects changes.

Quick Tricks

Use the speed-distance-time triangle

Place distance at the top and speed and time below it. Cover the required quantity to select the correct relation: D = S × T, S = D/T or T = D/S.

Example: For 150 km at 50 km/h, time = 150 ÷ 50 = 3 hours.
Convert units before calculating

Convert all quantities into compatible units before applying a formula. Use 5/18 for km/h to m/s and 18/5 for m/s to km/h.

Example: 54 km/h = 54 × 5/18 = 15 m/s.
Equal-distance average speed shortcut

For two equal distances travelled at speeds u and v, average speed = 2uv/(u + v). This is the harmonic mean, not (u + v)/2.

Example: At 30 km/h and 60 km/h over equal distances, average speed = 2 × 30 × 60/(30 + 60) = 40 km/h.
Relative speed for meeting or overtaking

Add speeds when two objects move towards each other. Subtract speeds when they move in the same direction.

Example: Two vehicles moving towards each other at 40 km/h and 50 km/h have relative speed 90 km/h.

Speed Time and Distance Concepts

Units and conversion of speed

Speed must be expressed in compatible units with distance and time before using the formula.

Since 1 km = 1000 m and 1 hour = 3600 seconds, 1 km/h = 1000/3600 m/s = 5/18 m/s. Therefore, km/h is converted to m/s by multiplying by 5/18, while m/s is converted to km/h by multiplying by 18/5.

Example: 72 km/h = 72 × 5/18 = 20 m/s. Also, 25 m/s = 25 × 18/5 = 90 km/h.

Average speed

Average speed equals total distance divided by total time.

For journeys with different distances or times, use Average speed = (d₁ + d₂ + ...) ÷ (t₁ + t₂ + ...). If equal distances are covered at speeds u and v, the formula becomes 2uv/(u + v). If equal times are spent at speeds u and v, average speed is (u + v)/2.

Example: A person travels 60 km at 30 km/h and another 60 km at 60 km/h. Total distance = 120 km and total time = 2 + 1 = 3 hours, so average speed = 120/3 = 40 km/h.

Relative speed

Relative speed is the speed of one object as observed from another moving object.

For objects moving in opposite directions, relative speed is the sum of their speeds. For objects moving in the same direction, it is the positive difference between their speeds. Meeting time or overtaking time is calculated as Relative distance ÷ Relative speed.

Example: A 120 m long train moving at 20 m/s overtakes a 10 m/s train moving in the same direction. Relative speed = 20 − 10 = 10 m/s, so the overtaking time is 120/10 = 12 seconds if only the first train's length is considered in the stated distance.

Train problems

For a train crossing an object, time equals the required crossing distance divided by the train's speed.

A train crossing a pole covers its own length. A train crossing a platform covers train length plus platform length. Two trains crossing each other cover the sum of their lengths. Use relative speed when both trains are moving.

Example: A 180 m train crosses a 120 m platform at 54 km/h. Its speed is 54 × 5/18 = 15 m/s, and distance covered is 180 + 120 = 300 m. Time = 300/15 = 20 seconds.

Boats and streams

The downstream speed of a boat is its still-water speed plus stream speed, while its upstream speed is the difference between them.

If the boat's speed in still water is b and the stream speed is s, downstream speed = b + s and upstream speed = b − s. Hence, b = (downstream speed + upstream speed)/2 and s = (downstream speed − upstream speed)/2.

Example: If downstream speed is 15 km/h and upstream speed is 9 km/h, still-water speed = (15 + 9)/2 = 12 km/h, and stream speed = (15 − 9)/2 = 3 km/h.

Speed Time and Distance Video Lessons

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11 Lessons
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TSD Basics: Distance Formula and Units

Learn the relationship D = S × T and understand how to convert common units of distance, speed, and time for solving basic Time, Speed and Distance problems.

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Practice Speed Time and Distance Questions

Practise published questions related to this topic.

1Simplify: √(2061 - √(1268 + √(850 - 66)))→ 2During a sale 50% of the goods are sold at 40% profit, 30% of the remaining goods are sold at 46% profit and the still remaining goods are sold at a loss of 24%. If there is an overall profit of x%, then what is the value of x?→ 3A shopkeeper sells an item for ₹430.5 after giving two successive discounts of 70% and 75% on its marked price. Had he not given any discount, he would have earned a profit of 40%. What is the cost price (in ₹) of the item?→ 4An 11-digit number 8732326687X is divisible by 18. What is the value of X?→ 5The H.C.F. and the L.C.M. of two numbers are 18 and 1296, respectively. If one of the numbers is 162, find the other one.→ 6What is the minimum value that must be assigned to A so that the 8-digit number 322A4828 is divisible by 4?→ 7A person sells an article at the loss of 10 percent. Cost price and selling price both are decreased by 20 percent. What will be the new loss percentage?→ 8Which of the following will have the highest selling price?→ 9An article is marked 25% above its cost price. A discount is offered so that a profit of 15% is made. Find the discount percentage.→ 10Selling price of an article is Rs. 336. Loss percentage is 30 percent. What is the cost price of the article?→

Speed Time and Distance Quick Quiz

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Quick Revision Notes

Speed Time and Distance Revision Points

Keep these relations and special cases ready for quick calculation.

  • Distance = Speed × Time; Speed = Distance ÷ Time; Time = Distance ÷ Speed.
  • 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h.
  • Average speed = Total distance ÷ Total time.
  • For equal distances at speeds u and v, average speed = 2uv/(u + v).
  • For equal travel times at speeds u and v, average speed = (u + v)/2.
  • Relative speed is the sum for opposite directions and the difference for the same direction.
  • A train crosses a pole over its own length and crosses a platform over train length plus platform length.
  • Downstream speed = boat speed + stream speed; upstream speed = boat speed − stream speed.

Speed Time and Distance FAQs

What is the speed distance formula?

Speed = Distance ÷ Time. The related formulae are Distance = Speed × Time and Time = Distance ÷ Speed.

How do you convert 90 km/h into m/s?

Multiply by 5/18: 90 × 5/18 = 25 m/s.

What is the average speed for equal distances at 40 km/h and 60 km/h?

Use 2uv/(u + v). Average speed = 2 × 40 × 60/(40 + 60) = 48 km/h.

When are speeds added in relative speed questions?

Speeds are added when two objects move in opposite directions or towards each other. For example, 30 km/h and 50 km/h give a relative speed of 80 km/h.

How is the time taken by a train to cross a platform calculated?

Time = (Train length + Platform length) ÷ Train speed. Convert the speed into m/s when lengths are given in metres.

What is the difference between downstream and upstream speed?

Downstream speed = boat speed in still water + stream speed. Upstream speed = boat speed in still water − stream speed.

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