A car is traveling at a speed of 80 kilometers per hour. What is the car’s speed in miles per hour? How many miles will the car travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers. Speed: Distance traveled in 5 hours: 01 mi h mi X
The correct answer and explanation is:
To solve this problem, we need to convert the car’s speed from kilometers per hour (km/h) to miles per hour (mph) and then determine the distance it will travel in 5 hours.
1. Convert the speed from kilometers per hour to miles per hour.
We know that:
- The car’s speed is 80 kilometers per hour.
- The conversion factor between kilometers and miles is 1 mile = 1.6 kilometers.
To convert the speed to miles per hour, we can use the following formula: Speed in mph=Speed in km/hConversion factor\text{Speed in mph} = \frac{\text{Speed in km/h}}{\text{Conversion factor}}
Substitute the given values: Speed in mph=80 km/h1.6\text{Speed in mph} = \frac{80 \, \text{km/h}}{1.6}
Now, calculate: Speed in mph=50 miles per hour\text{Speed in mph} = 50 \, \text{miles per hour}
So, the car’s speed is 50 miles per hour.
2. Determine the distance the car will travel in 5 hours.
Now, we need to calculate the distance the car will travel in 5 hours at the speed of 50 miles per hour. The formula for distance is: Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}
Substitute the values: Distance=50 miles per hour×5 hours\text{Distance} = 50 \, \text{miles per hour} \times 5 \, \text{hours}
Now, calculate: Distance=250 miles\text{Distance} = 250 \, \text{miles}
Final Answers:
- The car’s speed is 50 miles per hour.
- The car will travel 250 miles in 5 hours.
Explanation:
The first part of the problem involves converting the given speed from kilometers per hour (km/h) to miles per hour (mph). Since the conversion factor between kilometers and miles is given as 1 mile = 1.6 kilometers, we divide the speed in km/h by 1.6 to convert it to mph. The result is 50 mph.
In the second part, to find the distance the car travels in 5 hours, we use the basic formula for distance, which is speed multiplied by time. By multiplying the speed of 50 mph by the time of 5 hours, we find that the car will travel 250 miles in that period.
This demonstrates how unit conversions and basic formulas can be used to solve real-world motion problems effectively.