Jeff can walk comfortably at 4 miles per hour. Find a linear equation that represents the total distance Jeff can walk in t hours, assuming he doesn't take any breaks.
Answer (2)
The linear equation that represents the total distance Jeff can walk in t hours is d = 4 t , where d is the distance in miles and t is the time in hours. This equation uses the distance formula, which states that distance is equal to speed multiplied by time. Jeff's constant walking speed is 4 miles per hour, leading to this straightforward relationship between time and distance walked.
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Define the variables: Let d be the total distance and t be the time in hours.
Use the formula: distance = speed \times time.
Substitute the given speed: d = 4 \times t.
The linear equation is: d = 4 t .
Explanation
Problem Analysis Let's analyze the problem. We are given that Jeff walks at a constant speed of 4 miles per hour. We need to find a linear equation that represents the total distance Jeff can walk in t hours.
Distance Formula We know that distance is equal to speed multiplied by time. In this case, the speed is 4 miles per hour, and the time is t hours. So, we can write the equation as: distance = speed \times time
Finding the Equation Substituting the given speed, we get: distance = 4 \times t So, the linear equation representing the total distance Jeff can walk in t hours is d = 4t, where d is the distance in miles.
Final Equation Therefore, the linear equation that represents the total distance Jeff can walk in t hours is d = 4t
Examples
Imagine you are planning a road trip. If you know you'll be driving at a steady speed, like 60 miles per hour, you can use a linear equation to figure out how far you'll travel in a certain amount of time. For example, if you drive for 3 hours, the distance you cover is calculated as: distance = 60 \times 3 = 180 miles. This simple calculation helps you estimate travel times and plan your journey effectively, ensuring you arrive on schedule.
