A car is traveling at a speed of 60 kilometers per hour. What is the car’s speed in miles per hour? How many miles will the car travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers.
The correct answer and explanation is :
To convert the car’s speed from kilometers per hour (km/h) to miles per hour (mph), we use the given conversion factor:
[
1 \text{ mile} = 1.6 \text{ kilometers}
]
Step 1: Convert Speed to Miles per Hour
The car is traveling at 60 km/h. To convert this to miles per hour, we divide by 1.6:
[
60 \div 1.6 = 37.5 \text{ mph}
]
Thus, the car’s speed is 37.5 miles per hour.
Step 2: Calculate Distance Traveled in 2 Hours
Since the car is traveling at 37.5 mph, the distance it covers in 2 hours is:
[
37.5 \times 2 = 75 \text{ miles}
]
Thus, the car will travel 75 miles in 2 hours.
Explanation:
- Unit Conversion:
- The speed was originally given in kilometers per hour. Since we needed miles per hour, we used the conversion factor 1 mile = 1.6 km.
- We divided 60 km/h by 1.6 to get the equivalent speed in miles per hour.
- Distance Calculation:
- Once we found the speed in miles per hour (37.5 mph), we multiplied it by the time given (2 hours) to determine the total distance.
- Why This Works:
- This method ensures accurate unit conversion and maintains correct proportionality.
- Dividing by 1.6 accounts for the difference between kilometers and miles.
- Multiplying speed by time gives the total distance, following the basic formula: [
\text{Distance} = \text{Speed} \times \text{Time}
]
By using this systematic approach, we correctly determine that the car is traveling at 37.5 mph and will cover 75 miles in 2 hours.