What is the rate of change? Find the change in Marco’s distance each hour.
Understand the Problem
The question is asking for the rate of change in Marco's distance from the Grand Canyon as he drives. It involves understanding how much his distance changes each hour based on the information given about his driving speed and time.
Answer
The rate of change is $50$ miles per hour.
Answer for screen readers
The rate of change is $50$ miles per hour.
Steps to Solve
-
Determine distance decrease per hour Marco's distance from the Grand Canyon decreases by 150 miles every 3 hours. To find the rate of change per hour, we divide the distance decrease by the time.
$$ \text{Rate of change per hour} = \frac{150 \text{ mi}}{3 \text{ h}} = 50 \text{ mi/h} $$
-
Calculate the total distance decreased after 4 hours To find out how much Marco's distance decreases after 4 hours, we multiply the rate of change by the time driven.
$$ \text{Total distance decreased} = 50 \text{ mi/h} \times 4 \text{ h} = 200 \text{ mi} $$
-
Find initial distance from the Grand Canyon Since Marco's distance from the Grand Canyon after 4 hours is 200 miles, we add the total distance decreased to find the initial distance.
$$ \text{Initial distance} = 200 \text{ mi} + 200 \text{ mi} = 400 \text{ mi} $$
-
Confirm rate of change The rate of change, based on the initial information, confirms it is consistent throughout the trip. The consistent rate of change is key.
The rate of change is $50$ miles per hour.
More Information
Marco maintains a consistent driving speed, decreasing his distance to the Grand Canyon at a steady rate of 50 miles per hour. This means that, regardless of how much time passes, he covers the same distance decrease each hour.
Tips
- Confusing total distance driven with distance remaining: Make sure to distinguish between how far Marco has driven versus his remaining distance.
- Assuming the rate changes without evidence: The problem indicates a constant rate of distance change, which must be applied while solving.
AI-generated content may contain errors. Please verify critical information
