Chapter 4.6, Problem 24STP

3

To determine

The time (minutes) Tatiana must take to complete the final mile to reach her goal.

Answer to Problem 24STP

Tatiana will take 8.33 minutes to complete the final mile to reach her goal.

Explanation of Solution

Given information: It is given that,

The Tatiana runs a total of 5 miles by keeping her average 9 minutes per mile.

And after 4 miles her average pace is 9 minutes 10 seconds per mile.

Calculation: With the help of given data,

The total time taken by Tatiana to complete 5 miles is equal to 5 multiplied by 9.

  $\text{Time taken to complete 5 miles}=45\text{minutes}$

But according to question she completes first 4 miles at an average pace of 9 minutes 10 seconds per mile.

  $\begin{array}{c}\text{Original time taken for 4 miles}=\left(4\right)\left(9\text{'}10\text{'}\text{'}\right)\\ =\left(4\right)\left(9\frac{1}{6}\right)\\ =\left(4\right)\left(\frac{55}{6}\right)\\ =\frac{110}{3}\text{ minutes}\end{array}$

Therefore time taken in last mile is equal to 45 minutes minus original time $\left(\frac{110}{3}m\right)$ taken by her.

  $\begin{array}{c}\text{Time taken in last mile}=45-\frac{110}{3}\\ =\frac{135-110}{3}\\ =\frac{25}{3}\\ =8.33\text{ minutes}\end{array}$

Hence, she will complete her goal in 8.33 minutes.