Time, Speed and Distance: Formulas, Trains and Boats

These questions look varied but rest on one relationship: distance = speed × time.

The basics

• Speed = distance ÷ time
• Time = distance ÷ speed
• Distance = speed × time

Unit conversion

• km/h to m/s: multiply by 5/18.
• m/s to km/h: multiply by 18/5.

Example: 72 km/h = 72 × 5/18 = 20 m/s.

Average speed

For a journey with equal distances at speeds x and y:

Average speed = 2xy ÷ (x + y)

Example: going at 40 km/h and returning at 60 km/h gives 2 × 40 × 60 ÷ 100 = 48 km/h, not 50.

If the times are equal, the average is simply (x + y) ÷ 2.

Relative speed

• Same direction: subtract the speeds.
• Opposite directions: add the speeds.

Trains

• Crossing a pole or a person: time = length of train ÷ speed.
• Crossing a platform or bridge: time = (train length + platform length) ÷ speed.
• Two trains crossing: use the sum of lengths and the relative speed.

Example: a 150 m train at 54 km/h crosses a pole in 150 ÷ 15 = 10 seconds, since 54 km/h = 15 m/s.

Boats and streams

Let boat speed in still water be u and stream speed be v.

• Downstream speed = u + v
• Upstream speed = u − v
• Boat speed = (downstream + upstream) ÷ 2
• Stream speed = (downstream − upstream) ÷ 2

Common traps

1. Units. Convert to consistent units first.
2. Average speed. Do not take a simple average when distances are equal.
3. Train length. Remember to add lengths when crossing another object with length.

Tips

• Draw a quick sketch for train and boat questions.
• Write the unit beside each number.
• Check that the answer is realistic.

Practice

Regular short sets on this topic quickly build confidence, because the same few ideas repeat.

Practise with Online Exam Question & Answer →