Speed, Distance, and Time

Speed, distance, and time (SDT) problems appear frequently in QR, often embedded in timetable, journey planning, or data table scenarios. The mathematics is GCSE-level, but the time pressure and the need to convert units make these questions tricky under exam conditions. This lesson covers the core formulas, unit conversions, multi-leg journeys, and the common traps.

---

The Core Formulas

To Find	Formula
Distance	Speed × Time
Speed	Distance ÷ Time
Time	Distance ÷ Speed

Memory Aid: The SDT triangle. Place Distance at the top, Speed and Time at the bottom. Cover the quantity you want to find — the remaining two show the formula.

---

Unit Consistency

The most common source of error in SDT problems is mismatched units.

If Speed Is In...	Time Must Be In...	Distance Will Be In...
km/h	hours	km
mph	hours	miles
m/s	seconds	metres
km/min	minutes	km

Example: A car travels at 60 km/h for 45 minutes. How far does it travel?

• Wrong: 60 × 45 = 2,700 km (units don't match: km/h × minutes)
• Right: 45 minutes = 0.75 hours. Distance = 60 × 0.75 = 45 km

---

Converting Between Speed Units

km/h to m/s: ÷ 3.6

Why? 1 km/h = 1,000 m / 3,600 s = 1/3.6 m/s

km/h	÷ 3.6	m/s
36	÷ 3.6	10
72	÷ 3.6	20
108	÷ 3.6	30
90	÷ 3.6	25

m/s to km/h: × 3.6

m/s	× 3.6	km/h
5	× 3.6	18
15	× 3.6	54
25	× 3.6	90

mph to km/h: × 1.6 (approximate)

This conversion factor is approximate but sufficient for QR.

mph	× 1.6	km/h
30	× 1.6	48
60	× 1.6	96
70	× 1.6	112

---

Time Conversions for SDT

Minutes to Hours

Divide by 60:

• 15 minutes = 0.25 hours
• 20 minutes = 0.333 hours
• 30 minutes = 0.5 hours
• 45 minutes = 0.75 hours
• 90 minutes = 1.5 hours

Hours and Minutes to Decimal Hours

Example: 2 hours 40 minutes

• 40 ÷ 60 = 0.667
• Total: 2.667 hours

Decimal Hours to Hours and Minutes

Example: 3.4 hours

• 0.4 × 60 = 24 minutes
• Total: 3 hours 24 minutes

---

Average Speed

Average Speed = Total Distance ÷ Total Time

The Common Trap

Average speed is NOT the average of the individual speeds.

Example: A car drives 100 km at 50 km/h and then 100 km at 100 km/h.

Wrong: Average speed = (50 + 100) ÷ 2 = 75 km/h

Right:

• Time for leg 1: 100 ÷ 50 = 2 hours
• Time for leg 2: 100 ÷ 100 = 1 hour
• Total: 200 km in 3 hours
• Average speed = 200 ÷ 3 = 66.7 km/h

The average is lower than 75 because the car spent more time at the slower speed.

---

Multi-Leg Journeys

Many QR questions involve journeys with multiple legs, stops, or different speeds.

Method

1. Calculate distance, speed, or time for each leg separately
2. Sum distances and times as appropriate
3. Use totals to answer the question

Worked Example

Data: A delivery van travels:

• 40 km at 80 km/h to Town A
• Stops for 15 minutes in Town A
• 30 km at 60 km/h to Town B

Question: What is the total journey time?