A marathon runner ran 26.2 miles in 2 h 30 min. Find these rates:

a. miles per hour
b. miles per minute
c. minutes per mile

(a) miles per hour

26.2 / 2.5 = ?

(b) miles per minute: first convert 2.5 hours to minutes.
2.5 * 60 = 150 min
26.2 / 150 = ?

(c) minutes per mile: just get the reciprocal of your answer in (b)

a) 7.49 miles

b) 0.12 miles per minute

To find these rates, we need to convert the time and distance units to be consistent.

a. Miles per hour:
To find the miles per hour, we divide the total distance (26.2 miles) by the total time taken (2 hours and 30 minutes):

Total time = 2 hours + 30 minutes
= 2.5 hours

Rate = Distance / Time
= 26.2 miles / 2.5 hours
= 10.48 miles per hour (rounded to two decimal places)

So, the marathon runner's rate in miles per hour is approximately 10.48 mph.

b. Miles per minute:
To find the miles per minute, we need to convert the time to minutes. Since there are 60 minutes in an hour, we multiply the hour value by 60:

Total time in minutes = 2 hours x 60 minutes + 30 minutes
= 120 minutes + 30 minutes
= 150 minutes

Rate = Distance / Time
= 26.2 miles / 150 minutes
≈ 0.1747 miles per minute (rounded to four decimal places)

So, the marathon runner's rate in miles per minute is approximately 0.1747 miles/min.

c. Minutes per mile:
To find the minutes per mile, we divide the total time (150 minutes) by the total distance (26.2 miles):

Rate = Time / Distance
= 150 minutes / 26.2 miles
≈ 5.7252 minutes per mile (rounded to four decimal places)

So, the marathon runner's rate in minutes per mile is approximately 5.7252 min/mile.

To find the rates, we need to convert the time and distance into the appropriate units.

a. To find the rate in miles per hour, we need to divide the total distance of 26.2 miles by the time in hours.

To convert 2 hours and 30 minutes to hours, we can start by converting 30 minutes to hours. Since there are 60 minutes in an hour, we divide 30 minutes by 60:

30 minutes / 60 = 0.5 hours

Now we can add the converted minutes to the original hours:

2 hours + 0.5 hours = 2.5 hours

To find the rate in miles per hour, we divide the total distance of 26.2 miles by the time in hours:

26.2 miles / 2.5 hours ≈ 10.48 miles per hour

Therefore, the rate is approximately 10.48 miles per hour.

b. To find the rate in miles per minute, we divide the total distance of 26.2 miles by the time in minutes:

26.2 miles / 150 minutes = 0.1747 miles per minute

Therefore, the rate is approximately 0.1747 miles per minute.

c. To find the rate in minutes per mile, we divide the time in minutes by the total distance of 26.2 miles:

150 minutes / 26.2 miles ≈ 5.725 minutes per mile

Therefore, the rate is approximately 5.725 minutes per mile.