What is 3 miles + 7,568 yards + 1,056 feet? (Put your answer in miles and as a decimal.) (Conversion factors: 3 feet = 1 yard; 1,760 yards = 1 mile.)
The Correct Answer and Explanation is:
To solve this, we need to convert all the measurements to miles and then add them up.
Step 1: Convert yards and feet to miles
1. Convert 7,568 yards to miles:
- We know that 1 mile = 1,760 yards.
- To convert 7,568 yards to miles, divide the number of yards by 1,760.
7,568 yards1,760 yards per mile=4.3 miles\frac{7,568 \, \text{yards}}{1,760 \, \text{yards per mile}} = 4.3 \, \text{miles}1,760yards per mile7,568yards=4.3miles
2. Convert 1,056 feet to miles:
- We know that 3 feet = 1 yard and 1,760 yards = 1 mile.
- So, 1 foot = 1/3 yards. Therefore, 1,056 feet = 1,056 ÷ 3 = 352 yards.
- Now, convert the 352 yards to miles.
352 yards1,760 yards per mile=0.2 miles\frac{352 \, \text{yards}}{1,760 \, \text{yards per mile}} = 0.2 \, \text{miles}1,760yards per mile352yards=0.2miles
Step 2: Add everything up
Now, we can add the values: 3 miles+4.3 miles+0.2 miles=7.5 miles3 \, \text{miles} + 4.3 \, \text{miles} + 0.2 \, \text{miles} = 7.5 \, \text{miles}3miles+4.3miles+0.2miles=7.5miles
Final Answer:
So, the total distance is 7.5 miles.
This is how you perform the conversions and add the values correctly. By converting everything to miles, you ensure the units are consistent and can be added properly.
