Speed and Circles are a new topics that are introduced in primary 6. After the core topics of fractions, ratio, percentages and decimals, the next “mountains” to conquer are the topics of speed and circles. In this article, let’s talk about speed. With regards to speed questions, one must understand the relationship between distance, speed and time. A lot of students are taught the distance-speed-time triangle. That sums up the relationship between distance,speed and time. But are students able to apply?

Most of the time, students must be able to understand that the question gives two variables directly or indirectly and expects the student to figure out the third variable. For example, if the student is given the distance travelled by an object and the time taken by it, the student can figure out the third variable which is speed. Of course, this is an oversimplification of it.

Here are the various types of questions that a student must be able to answer.

**Journey by parts**

*A ship took 7 h to sail from port A to port B at an average speed of 42 km/h.
It then reduced its speed by 9 km/h and took another 11 h to sail from port B to port C.
Find the total distance covered by the ship.*

**– See more here**

*At 7 a.m. , a motorboat set off on its journey.
It sailed a distance of 162 km between beach A and beach B .
Its average speed between beach A and beach B was 27 km/h.
It then sailed 198 km from beach B to beach C at an average speed of 22 km/h.
What is the total time taken by the motorboat for the whole journey ?*

**– See more here**

Typically questions like these break the journey up into sections. This can be something that students find complicated.

**2 objects travelling towards each other**

*Islands X and Y are located 360 km apart.
Boat A starts from X in the direction of Y at an average speed of 44 km/h.
Simultaneously, boat B starts from Y towards X at an average speed of 28 km/h.
(a) If both boats took the same route , after how much time will the two boats meet ?
(b) How far would boat A have travelled when it met boat B ?
(c) How far would boat B have travelled when it met boat A ?*

**– See more here**

**2 objects travelling in opposite directions**

*From a point, a car and a lorry started moving in opposite directions along a straight road.
They were 400 km apart after having travelled for 4 h.
The average speed of the car was 45 km/h.
Find the average speed of the lorry.*

**– See more here**

**2 objects with different speeds where one overtakes the other eventually**

*Boat A started travelling at 10 a.m. at an average speed of 26 km/h.
Boat B, heading in the same direction, started from the same point at 12 noon.
If it took boat B 4 h to catch up with boat A, find the average speed of boat B.*

**– See more here**

**2 objects where one of the objects has an unknown speed**

*A motorcyclist set off from a city A to the airport.
By 4 p.m. , 3/5 of his journey was completed and at that time, he passed a cyclist who was also travelling in the same direction.
The average speed of the cyclist was 24 km/h.
By 6 p.m. , the motorcyclist reached his destination but the cyclist lagged behind by 12 km.
If the cyclist had also started from the city, how long would it take him to travel from the city to the airport ?*

*– See more here*

**The inverse relationship of time and speed when distance is held as a constant**

*It took Diana 48 minutes to walk from her house to the cinema.
It took Gina 1 hour 20 minutes to walk from Diana’s house to the cinema.
The difference between Diana’s walking speed and Gina’s walking speed was 2 km/h.
(a) How far was the cinema from Diana’s house?
(b) What was Diana’s walking speed?*

**– See more here**

Of course, there is much more. This is definitely not meant to be exhaustive. But once these concepts are mastered, the student attempting variations of these questions with mixed concepts should be able to find ways to solve them more easily.

Do remember that we have more than 10,000 math questions that you and your child can attempt, get scored for and even get progress tracked with our progress tracking tools. We also have more than 25 speed exercises that you can utilise to your benefit. Sharing and attempting is free and we’d like to keep it that way. We want all exam materials to be free. It should be.

Also, we have step by step worked video explanations to these questions and if you are interested, you’d be glad to know that it is a great tuition supplement and these videos really can help your child nail down her weaknesses and master all the advanced speed questions.

With Singapore Math Guru, you get instant access, 24/7, for just $39.90 a month! You can watch explainer videos to all the tough questions any time of the day, an replay it any number of times you need!

*For more tips and articles like this, book mark our blog and check back again real soon, or ‘Like’ us on Facebook! *

S*ign up with us** and let our video explanations guide your child! Each and every video explanation to our questions is a complete guide to getting full marks to every question. Did we mention that we have 300 hours of video solutions and explanations? Sign up now at www.singaporemathguru.com!*