Revision notes
What is rate?
A rate compares how one quantity changes with another quantity. In general,
$ \text{Rate: Quantity 1 per Quantity 2 = }$ $ { \text{Quantity 1} \over \text{Quantity 2} } $
Example
Harold views $10$ Instagram profiles in $8$ minutes. Find
(a) the number of minutes spent per profile,
Answer: $ 0.8 \text{ minutes per profile} $
(b) and the number of profiles viewed per minute.
Answer: $ 1.25 \text{ profiles per minute} $
Speed, distance and time formula
$ \text{Speed = }$ $ { \text{Distance} \over \text{Time} } $
$ \text{Average speed = }$ $ { \text{Total Distance} \over \text{Total Time} } $
Note: $ \text{Average speed } \ne \text{Average of two speeds} $
How to convert from m/s to km/h (and vice versa)
$ \text{1 km = }$ $ 1000 $$ \text{ m} $
$ \text{1 m = }$ $ 100 $$ \text{ cm} $
$ \text{1 minute = }$ $ 60 $$ \text{ seconds} $
$ \text{1 hour = }$ $ 60 $$ \text{ minutes = } $ $ 3600 $$ \text{ seconds} $
Example
(a) Convert $67$ m/s to km/h.
Answer: $ 241.2 \text{ km/h} $
(b) Convert $90$ km/h to m/s.
Answer: $ 25 \text{ m/s} $
Practice questions
Rate and speed word problems
1. A van travels from Town A to Town B, a distance of $180$ km, at an average speed of $20$ m/s.
(a) Find the time taken for the journey from Town A to Town B. Leave your answer in hours and minutes.
Answer: $ \text{2 hours 30 minutes} $
The van then travels from Town B to Town C at an average speed of $60$ km/h. The journey took $1$ hour and $20$ minutes.
(b) Find the average speed, in km/h, of the van for the entire journey from Town A to Town C.
Answer: $ 67.8 \text{ km/h} $
The van uses diesel at a rate of $8$ litres per $100$ km.
(c) If the van has $40$ litres of diesel at the start of the journey at Town A, find the amount of diesel left at the end of the journey at Town C.
Answer: $ 19.2 \text{ litres} $
How to solve train-and-tunnel speed problems
2. A train of length $120$ m travels at a constant speed of $18$ m/s. It enters a tunnel and takes $35$ seconds to pass completely through it. Find the length of the tunnel.
Answer: $ 510 \text{ m} $
O Level past year questions on rate
Fully worked, step-by-step solutions to these past-year questions (2016 to 2025) are in the O Level E Maths Solutions page. For 2015 and earlier, selected questions and their solutions are available to subscribers, linked individually in the table below.
| Year & paper | Comments |
|---|---|
| 2021 P1 Question 18a | Word problem on fuel consumption |
| 2019 P1 Question 23b | Word problem on amount of varnish required to paint the floor of a bedroom |
| 2011 P1 Question 6a | Word problem on filling glasses with water (Link 🔒 Subscribers) |
| 2011 P2 Question 2a | Word problem on fuel consumption |
| 2009 P1 Question 11 | Compare value of small can of soup vs. large can of soup (dollar per grams) |
O Level past year questions on speed
Fully worked, step-by-step solutions to these past-year questions (2016 to 2025) are in the O Level E Maths Solutions page. For 2015 and earlier, selected questions and their solutions are available to subscribers, linked individually in the table below.
| Year & paper | Comments |
|---|---|
| 2019 P2 Question 10 | Long word problem in real-world context (10 marks - last question of Paper 2) |
| 2018 P1 Question 10 | Word problem - Time difference between two countries |
| 2017 P2 Question 10 | Long word problem in real-world context (10 marks - last question of Paper 2) |
| 2014 P1 Question 18 | (a) Convert km/h to m/s (b) Time taken for train to pass the tunnel (Link 🔒 Subscribers) |
| 2013 P1 Question 8 | Word problem |
| 2010 P1 Question 21 | Word problem |
| 2008 P1 Question 4 | Word problem |
| 2007 P1 Question 20 | Word problem |
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