Time and Work, Speed and Distance Problems

In science and mathematics, we frequently encounter situations where quantities like time, work, speed, and distance are connected. Understanding how these quantities relate to one another is a powerful reasoning tool — whether you're calculating how long a chemical reaction takes, how fast a vehicle travels, or how much work multiple machines can do together.

These problem types appear across physics, chemistry, biology, and everyday life. The key skill is identifying which quantities you know and which you need to find, then selecting the correct relationship to connect them.

In this subtopic, you will learn to:

• Apply the speed-distance-time relationship
• Solve work-rate problems involving one or more workers
• Use proportional reasoning to tackle complex scenarios
• Interpret and communicate your solutions clearly

The fundamental relationship between speed, distance, and time is:

$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$

This can be rearranged into three forms depending on which variable you need:

$\text{Distance}=\text{Speed}\times \text{Time}$

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

A helpful memory tool is the DST triangle (also called the formula triangle):

How to use the triangle:

• Cover the quantity you want to find
• What remains shows you the operation: side by side = multiply, one on top of other = divide