A car is traveling at a rate of 80 kilometers per hour. What is the car’s rate in miles per hour? How many miles will the car travel in 3 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
The Correct Answer and Explanation is:
Problem Breakdown and Solution
Given:
- The car’s speed is 80 kilometers per hour (km/h).
- The conversion factor between kilometers and miles is 1 mile = 1.6 kilometers.
- The task is to find the car’s rate in miles per hour (mph), and the distance the car will travel in 3 hours.
Step 1: Convert kilometers per hour (km/h) to miles per hour (mph)
To convert the car’s speed from kilometers per hour to miles per hour, use the conversion factor. Since 1 mile equals 1.6 kilometers, we divide the speed in kilometers per hour by 1.6 to obtain the speed in miles per hour.
[
\text{Speed in miles per hour} = \frac{\text{Speed in kilometers per hour}}{1.6}
]
Substitute the given speed of 80 km/h into the formula:
[
\text{Speed in miles per hour} = \frac{80}{1.6} = 50 \, \text{mph}
]
Step 2: Calculate the distance the car will travel in 3 hours
To determine how many miles the car will travel in 3 hours, multiply the speed in miles per hour by the time in hours. We already know the speed is 50 mph, and the time is 3 hours.
[
\text{Distance} = \text{Speed} \times \text{Time}
]
Substitute the values:
[
\text{Distance} = 50 \times 3 = 150 \, \text{miles}
]
Final Answer:
- The car’s rate is 50 miles per hour.
- The car will travel 150 miles in 3 hours.
Explanation
To solve this problem, we started by converting the car’s speed from kilometers per hour to miles per hour. This conversion is essential because the problem asks for the car’s rate in miles per hour. We used the conversion factor of 1 mile = 1.6 kilometers, which means that for every 1.6 kilometers, the car travels 1 mile. Thus, dividing the speed in kilometers per hour by 1.6 converts it to miles per hour.
Next, to calculate the distance the car travels in a given time, we applied the basic formula for distance:
[
\text{Distance} = \text{Speed} \times \text{Time}
]
By multiplying the car’s speed in miles per hour (50 mph) by the time (3 hours), we obtained the total distance traveled, which is 150 miles. This method involves basic unit conversion and application of a simple distance formula.