Skill: Represent problems with tables

A table helps you organize the information in a problem. Label each row or column with what it represents, then look for how the quantities are related.

Example:
A cyclist travels $12$ miles in $2$ hours at a steady speed. How far will the cyclist travel in $5$ hours?

Step 1: Identify the quantities

The two quantities are:

• time, measured in hours
• distance, measured in miles

Make a table with one row for each quantity:

Time (hours)	$1$	$2$	$5$
Distance (miles)	?	$12$	?

Step 2: Find the relationship

The cyclist travels $12$ miles in $2$ hours. Find the distance traveled in $1$ hour:

$$12 \div 2 = 6$$

So the cyclist travels $6$ miles per hour.

The relationship is multiplicative:

$$\text{distance} = \text{hours} \times 6$$

Fill in the table:

Time (hours)	$1$	$2$	$5$
Distance (miles)	$6$	$12$	$30$

Step 3: Find the missing value

For $5$ hours:

$$5 \times 6 = 30$$

The cyclist will travel $30$ miles in $5$ hours.

The table makes the relationship visible: each number of hours is multiplied by $6$ to find the matching distance.