# Speed, Distance and Time

> Use the speed triangle, work with minutes and fractions of an hour, and solve train and meeting problems.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/speed-distance-time/. Updated 3 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The road trip
The Wilson family drives from Sydney to Canberra. The sign says "Canberra 280 km". Dad sets the cruise control to 100 km/h.

"Are we there yet?" asks Max after an hour. Mum does the maths: at 100 km/h they cover 100 km every hour. After 1 hour they have done 100 km, with 180 km to go. That is 1.8 more hours, or 1 hour 48 minutes.

**Speed** tells you how far you go in each unit of time. Knowing two of speed, distance and time lets you find the third.

**In short:** Speed, distance and time are linked: distance = speed × time, speed = distance ÷ time, and time = distance ÷ speed. Make sure the units match, so a speed in km/h needs the time in hours.

## Before you start

- Fractions of an hour: $\frac{1}{2}$ h $= 30$ min, $\frac{1}{4}$ h $= 15$ min, 1 min $= \frac{1}{60}$ h (see Metric Units and Conversions).
- Multiplying and dividing decimals.
- **km/h** means kilometres per hour: how many kilometres in one hour.

## The speed triangle

### Key idea: Three formulas, one triangle
$$\text{distance} = \text{speed} \times \text{time}$$

$$\text{speed} = \frac{\text{distance}}{\text{time}} \qquad \text{time} = \frac{\text{distance}}{\text{speed}}$$

Picture a triangle with D on top and S and T underneath. Cover the one you want: D is S times T, S is D over T, and T is D over S.

### Worked example: Distance
$2\frac{1}{2}$ hours at 90 km/h: $D = 90 \times 2.5 = 225$ km.

### Worked example: Time
150 km at 120 km/h: $T = \frac{150}{120} = 1.25$ h $= 1\frac{1}{4}$ h $= 1$ h 15 min.

### Worked example: Speed
A car goes 160 km in 4 hours: $S = \frac{160}{4} = 40$ km/h.

## Minutes and km/h

### Key idea: Turn minutes into a fraction of an hour
30 min $= \frac{1}{2}$ h, 20 min $= \frac{1}{3}$ h, 15 min $= \frac{1}{4}$ h, 6 min $= \frac{1}{10}$ h.

### Worked example: Short trips
30 minutes at 75 km/h: $75 \times \frac{1}{2} = 37.5$ km.

6 minutes at 100 km/h: $100 \times \frac{1}{10} = 10$ km.

40 minutes at 93 km/h: $93 \times \frac{2}{3} = 62$ km.

### Exam tip: Per minute trick
60 km/h is exactly 1 km per minute. So 20 minutes at 60 km/h is 20 km, and 90 km/h is 1.5 km per minute.

### Watch out: Units must match
If the speed is in km/h, the time must be in **hours**. "15 minutes at 80 km/h" is not $80 \times 15$. It is $80 \times \frac{1}{4} = 20$ km.

## km/h to metres per second

1 km/h $= 1000$ m in $3600$ seconds. So to change km/h into m/s, divide by 3.6.

$36$ km/h $= 36 \div 3.6 = 10$ m/s.

## Trains and tunnels

### Worked example: The whole train must pass
A goods train 180 m long travels at 36 km/h. How long does it take to pass completely through a station 90 m long, from when the front enters?

The **front** must travel the station's length **plus** the train's own length, so that the back clears the end: $90 + 180 = 270$ m.

Speed $= 10$ m/s, so time $= 270 \div 10 = 27$ seconds.

## Meeting problems

When two people move **towards each other**, the gap closes at the **sum** of their speeds.

### Challenge: Selective level: meeting in the middle
Two cyclists start 60 km apart and ride towards each other at 12 km/h and 18 km/h. The gap closes at 30 km/h, so they meet after $60 \div 30 = 2$ hours.

Two boys walk towards each other. The second boy's step is 80 cm, and the first boy's step is $\frac{13}{16}$ as long, which is 65 cm. They meet after 224 steps each. Each pair of steps closes the gap by $80 + 65 = 145$ cm. Total: $224 \times 145 = 32\,480$ cm, which is $324.8$ m.

**Mind map**

```text
Speed, distance, time
  Formulas
    D = S x T
    S = D ÷ T
    T = D ÷ S
  Units
    km/h needs hours
    Minutes into fractions of an hour
    km/h ÷ 3.6 = m/s
  Trains
    Station length + train length
  Meeting
    Towards each other: add speeds
```

## Quick summary

- Distance $=$ speed $\times$ time. Speed $=$ distance $\div$ time. Time $=$ distance $\div$ speed.
- Match the units: km/h needs time in hours.
- 30 min $= \frac{1}{2}$ h, 20 min $= \frac{1}{3}$ h, 15 min $= \frac{1}{4}$ h, 6 min $= \frac{1}{10}$ h.
- 60 km/h is 1 km per minute.
- A train passing through a station travels the station length plus its own length.
- Moving towards each other, add the speeds.

## Quiz

Try these questions from the chapter quiz.

1. A car travels at 40 km/h for 4 hours. How far does it go?
   - A. 10 km
   - B. 44 km
   - C. 160 km
   - D. 400 km
   - Answer: C. 160 km. $D = 40 \times 4 = 160$ km.

2. How far do you travel in 20 minutes at 60 km/h?
   - A. 3 km
   - B. 20 km
   - C. 40 km
   - D. 1200 km
   - Answer: B. 20 km. 60 km/h is 1 km per minute, so 20 km.

3. A car covers 210 km at 60 km/h. How long does it take?
   - A. 3 hours
   - B. 3.5 hours
   - C. 4 hours
   - D. 2.5 hours
   - Answer: B. 3.5 hours. $T = 210 \div 60 = 3.5$ h.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/speed-distance-time/#quiz