If we identify two quantities in a problem and one quantity is proportional to the other, then we can calculate the constant of proportionality and use it to answer other questions about the situation. For example, Andre runs at a constant speed of 5 meters every 2 seconds. How long does it take him to run 91 meters at this rate?
In this problem there are two quantities, time (in seconds) and distance (in meters). Since Andre is running at a constant speed, time is proportional to distance. We can make a table with distance and time as column headers and fill in the given information.
| distance (meters) | time (seconds) |
|---|---|
| 5 | 2 |
| 91 |
To find a value in the right column, we multiply the value in the left column by 52 because 52 ⋅5 =2. This means that it takes Andre 52 of a second to run 1 meter.
At this rate, it would take Andre 52⋅91=5182, or 36.4, seconds to walk 91 meters. More generally, if t is the time it takes to walk d meters at that pace, then t=52d.