Short Answer 
The distance formula relates distance, speed, and time as distance = speed √ó time. In this scenario, by solving the equations derived from two different speeds, it was determined that the store is located 3/5 of a mile away.
Step 1: Understand the Distance Formula
The relationship between distance, speed, and time is expressed by the formula distance = speed √ó time. To find out how far something is, you need to know both the speed at which it is traveling and the amount of time it has traveled. For this scenario, we are working with a speed of 6 miles per hour and a time variable denoted as t in hours.
Step 2: Set Up the Equation
In this problem, the distance can be expressed using two different speeds, leading to the equation d = 6t and d = 4(0.25 – t). Here, 0.25 hours corresponds to 15 minutes. The goal is to solve for t by equating the two distance expressions and simplifying the equation:
- Set the equations equal: 6t = 4(0.25 – t)
- Simplify and solve: 6t + 4t = 1, which leads to 10t = 1.
Step 3: Calculate the Distance
After solving for t, we find that t = 1/10 of an hour. To determine the distance to the store, we substitute t back into the distance formula d = 6t. Calculating this gives us d = 6(1/10), resulting in:
- Distance = 6/10 or 3/5 of a mile.
This means that the store is located 3/5 of a mile away.