To determine the writing speed of 150 words in 3 minutes, we calculate the rate in words per minute, which is found by dividing the total number of words by the total time in minutes. Here, we have $150$ words and $3$ minutes. Therefore, the calculation is as follows:

This indicates that the writing speed is $50$ words per minute.

Understanding rates is a crucial concept in mathematics, particularly in real-life applications. A rate quantifies how one quantity changes in relation to another. In this scenario, the quantities we are examining are the number of words and the time taken to write them. By dividing the total number of words by the total time in minutes, we can ascertain how many words are produced each minute.

This principle can be applied to a variety of contexts, such as calculating speed (distance over time), flow rates (volume over time), and heart rates (beats per minute). Practicing these calculations will enhance your comfort with the concept of rates and their relevance in everyday situations.

When tackling problems involving rates, it is essential to ensure that your units are consistent. In this example, we used words and minutes, but it’s also possible to express rates in other units, such as words per second or words per hour, depending on the context. Just be sure to adjust your calculations accordingly to maintain the accuracy of your results.