Question

nessie can run 12 miles in 89 minutes. she is thinking about running in two different races, a 9 - mile race and a 13 - mile race. at her current pace, how many more minutes will it take her to complete the 13 - mile race than the 9 - mile race?
minutes
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Explanation:

Step1: Find time for 9 - mile race

First, we know that speed is constant (since it's her current speed). Speed \( v=\frac{\text{distance}}{\text{time}} \). For the 9 - mile race, time \( t_1 = 126\) minutes, distance \( d_1=9\) miles. So speed \( v=\frac{9}{126}=\frac{1}{14}\) miles per minute.

Step2: Find time for 13 - mile race

Now, for the 13 - mile race, distance \( d_2 = 13\) miles, speed \( v=\frac{1}{14}\) miles per minute. Using \( t=\frac{d}{v}\), we have \( t_2=\frac{13}{\frac{1}{14}}=13\times14 = 182\) minutes.

Step3: Find the difference in time

The difference in time between the 13 - mile race and the 9 - mile race is \( t_2 - t_1=182 - 126 = 56\) minutes.

Answer:

56