Exercise 68 Page 31

Since the times are all recorded in Minutes:Seconds, the first step we need to take is to convert the times into seconds. Remember, $1$ minute = $60$ seconds, so we will multiply the minutes of each time by $60$ and add the seconds. Let's convert the first time to seconds together. First, let's convert the minutes to seconds. Then we add the seconds from the original time.

$$\begin{array}{c}22\cdot 60=1320\text{seconds}\\ 1320+31=1351\text{seconds}\end{array}$$

We found that $22\text{:}31$ equates to $1351$ seconds. Now we will reproduce our table applying the same process to all meet times.

Cross Country Meet Times
Meet	Time	Time in Seconds
$1$	$22\text{:}31$	$1351$
$2$	$22\text{:}21$	$1341$
$3$	$21\text{:}48$	$1308$
$4$	$22\text{:}01$	$1321$
$5$	$21\text{:}48$	$1308$
$6$	$20\text{:}56$	$1256$
$7$	$20\text{:}34$	$1236$
$8$	$20\text{:}15$	$1215$

The mean of a data set is calculated by finding the sum of all values in the set and then dividing by the number of values in the set. In this case, there are $8$ values in the set.

$\text{Mean}=\frac{\text{Sum of values}}{\text{Number of values}}$

SubstituteValues

Substitute values

$\text{Mean}=\frac{1351+1341+\dots +1215}{8}$

AddTerms

Add terms

$\text{Mean}=\frac{10336}{8}$

CalcQuot

Calculate quotient

$\text{Mean}=1292$

Now we need to convert the number of minutes back into the original Minutes:Seconds ratio. If we divide the value above by $60,$ the quotient will be the number of minutes, while the remainder will be the number of seconds.

$\frac{1292}{60}$

FracToMixed

Write fraction as a mixed number

$21\frac{32}{60}$

Blanca's mean time was $21\text{:}32.$