Problem 31 - Prealgebra

Question

Use the rate equation \(d=r \cdot t\) to solve. At 2: 30 P.M. Shelly leaves her house and drives at an average speed of 55 miles per hour to her sister's house. She arrives at 6: 30 p.m. a. How many hours was the drive to her sister's house? b. How many miles from her sister does Shelly live?

Step-by-Step Solution

Answer

a. 4 hours; b. Shelly lives 220 miles from her sister.

Step 1: Calculate the duration of travel

To find out how many hours Shelly was driving, subtract the start time of her journey, 2:30 PM, from the arrival time, 6:30 PM. 6:30 PM - 2:30 PM is 4 hours. Therefore, Shelly drove for 4 hours.

Step 2: Apply the rate equation

Now, use the rate equation, which is given by \( d = r \cdot t \), where \( d \) is the distance traveled, \( r \) is the rate (speed), and \( t \) is the time. Plug in the known values: rate \( r = 55 \) miles per hour and time \( t = 4 \) hours. This gives \( d = 55 \cdot 4 \).

Step 3: Calculate the distance

Calculate the multiplication \( 55 \times 4 = 220 \). Thus, the distance, \( d \), that Shelly traveled is 220 miles.

Key Concepts

Distance Calculation

Distance calculation is a fundamental concept in physics and everyday problem-solving involving movement from one point to another. When calculating distance, it is essential to use the rate equation, which provides a straightforward way to determine how far an object, like Shelly in our scenario, has traveled. The rate equation is given by:\[ d = r \cdot t \]where:

• \( d \) represents distance
• \( r \) is the rate, or the speed of travel
• \( t \) is the time spent traveling

Applying this equation allows us to find the unknown distance by multiplying the speed at which the object travels by the time it was in motion. For instance, Shelly's average speed was 55 miles per hour, and she drove for 4 hours. Plugging these values into the equation:\[ d = 55 \cdot 4 = 220 \]This shows Shelly traveled 220 miles.

Time Calculation

Calculating time accurately is crucial for understanding how long an activity such as a drive will take. In the context of Shelly's journey, time calculation helps determine the total duration of her drive. To find the time Shelly spent traveling, we need to subtract the start time from the arrival time. Shelly left her house at 2:30 PM and reached the destination at 6:30 PM. By performing the subtraction, we find: 6:30 PM - 2:30 PM = 4 hours This straightforward calculation confirms that Shelly's journey lasted 4 hours.