ASK YOUR TEACHER Which is longer, a 1300-meter race or a 1-mile race? (Use 1000 meters = 0.62137 mile.) 1300-meter race 1-mile race By how much? (Use 1000 meters = 0.62137 mile. Round your answer to the nearest whole number.) ___m By how much? (Use 1 meter = 3.28084 feet and 1 mile = 5280 feet. Round your answer to the nearest whole number.) ___m
The Correct Answer and Explanation is:
To compare the lengths of a 1300-meter race and a 1-mile race, we need to first convert the 1300 meters into miles using the conversion factor:
1 kilometer (1000 meters) = 0.62137 miles.
Step 1: Convert 1300 meters to miles
First, divide 1300 by 1000 to convert the 1300 meters into kilometers, and then multiply by the conversion factor to get the result in miles:1300 m×0.62137 mile1000 m=0.807781 miles1300 \, \text{m} \times \frac{0.62137 \, \text{mile}}{1000 \, \text{m}} = 0.807781 \, \text{miles}1300m×1000m0.62137mile=0.807781miles
Step 2: Compare the two distances
Now, we compare the 1300-meter race with a 1-mile race.
The 1300-meter race is approximately 0.8078 miles, which is less than 1 mile. So, the 1300-meter race is shorter.
To find out by how much shorter it is, subtract the length of the 1300-meter race from 1 mile:1−0.807781=0.192219 miles1 – 0.807781 = 0.192219 \, \text{miles}1−0.807781=0.192219miles
Step 3: Convert the difference to meters
To convert the difference back into meters, multiply the difference in miles by 1000:0.192219 miles×1000 miles/km=192.2 meters0.192219 \, \text{miles} \times 1000 \, \text{miles/km} = 192.2 \, \text{meters}0.192219miles×1000miles/km=192.2meters
Rounding this to the nearest whole number, the 1300-meter race is 192 meters shorter than the 1-mile race.
Step 4: Convert the difference to feet
To convert the 192.2 meters difference into feet, use the conversion factor 1 meter = 3.28084 feet:192.2 m×3.28084 feet/m=631.8 feet192.2 \, \text{m} \times 3.28084 \, \text{feet/m} = 631.8 \, \text{feet}192.2m×3.28084feet/m=631.8feet
Rounding this to the nearest whole number, the 1300-meter race is 632 feet shorter than the 1-mile race.
Summary of Results
- The 1300-meter race is 192 meters shorter than the 1-mile race.
- The 1300-meter race is 632 feet shorter than the 1-mile race.
By following these steps and using the conversion factors, we can easily compare the two races and calculate the difference in both meters and feet.
