Max completed a 10 mile run 1 hour 20 minutes. Which dimensional analysis would you use to find her average speed in miles per hour?
To find the average speed in miles per hour, we need to convert the time from 1 hour 20 minutes to hours.
1 hour 20 minutes can be written as 1.33 hours (since there are 60 minutes in an hour, and 20 minutes is 20/60 = 0.33 hours).
Now we can use dimensional analysis:
10 miles / 1.33 hours = (10 miles) / (1.33 hours) = 7.52 miles/hour
So the average speed is 7.52 miles per hour.
To find Max's average speed in miles per hour, we need to convert the time from hours and minutes to just hours. We can use dimensional analysis by setting up a conversion factor.
Conversion factor: 1 hour = 60 minutes
Given: 1 hour 20 minutes
Step 1: Convert 1 hour 20 minutes to just minutes:
1 hour = 60 minutes
1 hour 20 minutes = 1 × 60 + 20 = 80 minutes
Step 2: Convert 80 minutes to hours using the conversion factor:
80 minutes × (1 hour / 60 minutes) = 80/60 = 4/3 hours
Step 3: Divide the distance (10 miles) by the time (4/3 hours) to find the average speed in miles per hour:
10 miles / (4/3) hours = 10 × (3/4) miles per hour = 30/4 miles per hour = 7.5 miles per hour.
So, Max's average speed is 7.5 miles per hour.
To find Max's average speed in miles per hour, we can use dimensional analysis. Dimensional analysis is a technique that involves setting up a conversion factor to convert from one unit to another.
In this case, we need to convert from miles per minute (max's speed in the given time) to miles per hour. Here's how we can set up the conversion:
Step 1: Start with the given value:
Max's speed = 10 miles / 1 hour 20 minutes
Step 2: Convert the time to a decimal form:
1 hour 20 minutes = 1 + 20/60 = 1 + 1/3 = 4/3 hours
Step 3: Write the conversion factor:
1 hour = 60 minutes
Step 4: Set up the dimensional analysis equation:
Max's speed = 10 miles / (4/3 hours)
To simplify the equation, we can multiply the numerator and denominator by 3 to get rid of the fraction:
Max's speed = (10 miles * 3) / (4 hours)
Max's speed = 30 miles / 4 hours
Step 5: Divide to find Max's average speed:
Max's average speed = 30 miles / 4 hours
So, using dimensional analysis, Max's average speed is 30 miles per 4 hours, which simplifies to 7.5 miles per hour.