IGCSE · Practice questions · Rates, average speed and best value

Read the units.

Six original Cambridge-style questions on rates: speed, pay, flow, density and a multi-stage journey.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Write the rate with its units.

Units first: km/h means km ÷ h; that tells you whether to multiply or divide.
Time in hours: minutes ÷ 60, so 15 min $= 0.25$ h.
Average speed $=$ total distance ÷ total time, including stops.
Given formulas (density, pressure): substitute with consistent units.
Check that the answer is sensible and has units.

Recall

[1 marks]

Convert 15 m/s into km/h.

$15 \times 3600 = 54\,000$ m per hour $= 54$ km/h. ✓

Calculation

[2 marks]

A runner completes 21 km in 1 hour 45 minutes. Calculate her average speed in km/h.

1 hour 45 minutes $= 1.75$ h. ✓
$21 \div 1.75 = 12$ km/h. ✓

Calculation

[2 marks]

Water flows into a bath at 8.5 litres per minute. How long does it take to put 680 litres in the bath? Give your answer in hours and minutes.

$680 \div 8.5 = 80$ minutes. ✓
80 minutes $= 1$ hour 20 minutes. ✓

Calculation

[2 marks]

A country has a population of 3.6 million and an area of 4500 km². Population density $= \dfrac{\text{population}}{\text{area}}$. Calculate the population density.

$3\,600\,000 \div 4500 = 800$. ✓
800 people per km². ✓

Analysis

[3 marks]

Mia is paid $\$15.20$ per hour for her first 40 hours each week. Overtime is paid at 1.5 times the normal rate. One week she works 46 hours. Calculate her pay for the week.

Normal pay: $40 \times 15.20 = \$608$. ✓
Overtime rate: $1.5 \times 15.20 = \$22.80$; overtime pay: $6 \times 22.80 = \$136.80$. ✓
Total: $608 + 136.80 = \$744.80$. ✓

Analysis

[3 marks]

Raj drives 150 km at an average speed of 75 km/h. He stops for 30 minutes, then drives a further 100 km in 1 hour 30 minutes.

Calculate his average speed for the whole journey, including the stop.

First part: $150 \div 75 = 2$ h. ✓
Total time $= 2 + 0.5 + 1.5 = 4$ h; total distance $= 150 + 100 = 250$ km. ✓
Average speed $= 250 \div 4 = 62.5$ km/h. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.