Question

cel preview - 3.5 marathons
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1. fill in the table by converting the marathon times from hours into minutes. then use the

distance above to compute the rates (2 decimal places):
a. minutes per mile
b. miles per minute
c. miles per hour

1. the first cell in the table for minutes is h10.

Explanation:

Step1: Convert hours to minutes

Since \(1\) hour \( = 60\) minutes.
For \(2.92\) hours: \(2.92\times60=175.2\) minutes.
For \(2.88\) hours: \(2.88\times60 = 172.8\) minutes.
For \(2.78\) hours: \(2.78\times60=166.8\) minutes.

Step2: Calculate minutes per mile (\(a\))

The formula is \(\text{Minutes per mile}=\frac{\text{Total minutes}}{\text{Distance (miles)}}\).
Given distance \(d = 26.21875\) miles.
For \(175.2\) minutes: \(\frac{175.2}{26.21875}\approx6.68\)
For \(172.8\) minutes: \(\frac{172.8}{26.21875}\approx6.59\)
For \(166.8\) minutes: \(\frac{166.8}{26.21875}\approx6.36\)

Step3: Calculate miles per minute (\(b\))

The formula is \(\text{Miles per minute}=\frac{\text{Distance (miles)}}{\text{Total minutes}}\).
For \(175.2\) minutes: \(\frac{26.21875}{175.2}\approx0.15\)
For \(172.8\) minutes: \(\frac{26.21875}{172.8}\approx0.15\)
For \(166.8\) minutes: \(\frac{26.21875}{166.8}\approx0.16\)

Step4: Calculate miles per hour (\(c\))

The formula is \(\text{Miles per hour}=\frac{\text{Distance (miles)}}{\text{Total hours}}\).
For \(2.92\) hours: \(\frac{26.21875}{2.92}\approx9.0\)
For \(2.88\) hours: \(\frac{26.21875}{2.88}\approx9.10\)
For \(2.78\) hours: \(\frac{26.21875}{2.78}\approx9.43\)

Answer:

Hours	Minutes	Minutes/Mile	Miles/Minute	Miles/Hour
\(2.88\)	\(172.8\)	\(6.59\)	\(0.15\)	\(9.10\)
\(2.78\)	\(166.8\)	\(6.36\)	\(0.16\)	\(9.43\)