How to Calculate Rate of Change in Waiting Times

Calculating the rate of change is an important skill in understanding how values change over time. In this specific example, we are examining waiting times at a doctor's office over a three-month period: April, May, and June. Let's break down the steps to find the rate of change from April to June.

First, we look at the average waiting times:
- **April**: 56 minutes
- **May**: 56 minutes
- **June**: 50 minutes

The question asks, "What was the rate of change between April and June?" To answer this, we need to identify the change in waiting times and the time period over which this change occurred.

### Step 1: Calculate the Change in Waiting Time
To find the change in waiting time, we subtract the waiting time in June from the waiting time in April:
- **Change in Waiting Time** = Waiting Time in June - Waiting Time in April
- **Change in Waiting Time** = 50 minutes - 56 minutes = **-6 minutes**.
This negative value indicates that the waiting time decreased by 6 minutes.

### Step 2: Determine the Time Period
Next, we need to calculate how many months passed from April to June. The months are:
- **April** to **May** (1 month)
- **May** to **June** (1 month)
Thus, the total time period is 2 months.

### Step 3: Calculate the Rate of Change
Now we can compute the rate of change using the formula:
- **Rate of Change** = Change in Waiting Time ÷ Change in Number of Months
Substituting in our values:
- **Rate of Change** = -6 minutes ÷ 2 months = **-3 minutes per month**.

This means that, on average, the waiting time decreased by 3 minutes each month from April to June.

### Real-World Application
Understanding the rate of change is not only useful in math but also in real life. For instance, if you are tracking the time it takes to complete a task, knowing the rate of change can help you improve efficiency. If waiting times at a doctor's office decrease consistently, it may indicate that the office is becoming more efficient in managing patient flow.

### Conclusion
In summary, the correct rate of change from April to June is **-3 minutes per month**, indicating a steady decrease in waiting times. If you had mistakenly thought the rate was -6 minutes per month, consider that over 2 months, this would imply a drop of 12 minutes, which does not align with the data provided. Always ensure to check your calculations and understand the context of the values you are working with. This approach will help you in various mathematical and real-world applications.