Question

noorviper runs 10 miles a day. she is thinking about running in two different races: a 9 - mile race and a 13 - mile race. at her current rate, how many more minutes will it take her to complete the 13 - mile race than the 9 - mile race?

Explanation:

Step1: Identify the problem

We need to find how many more minutes Naomi will take to complete a 13 - mile race than a 9 - mile race. But we are missing her running speed (miles per minute or minutes per mile). Let's assume we know her minutes per mile, say \(r\) minutes per mile (the number of minutes she takes to run 1 mile).

Step2: Time for 9 - mile race

The time taken to run a 9 - mile race, \(T_9\), is the number of miles times the time per mile. So \(T_9=9\times r = 9r\) minutes.

Step3: Time for 13 - mile race

The time taken to run a 13 - mile race, \(T_{13}\), is \(T_{13}=13\times r=13r\) minutes.

Step4: Difference in time

The difference in time \(\Delta T=T_{13}-T_9\). Substitute the values of \(T_{13}\) and \(T_9\): \(\Delta T = 13r-9r=(13 - 9)r = 4r\) minutes.

Since the problem is not fully provided (we need the value of \(r\), her minutes per mile), if we assume, for example, if she runs 1 mile in \(x\) minutes, the difference is \(4x\) minutes. If we had a specific value for \(x\) (like if she runs 1 mile in 10 minutes, the difference would be \(4\times10 = 40\) minutes), but since the problem is incomplete, we can only provide the formula for the difference.

Answer:

Let \(r\) be the number of minutes Naomi takes to run 1 mile. The number of additional minutes she takes for the 13 - mile race compared to the 9 - mile race is \(4r\) minutes. If a specific value of \(r\) is given (e.g., if \(r = 10\) minutes per mile, the answer is \(40\) minutes), but with the current information, the general formula is \(4r\) minutes.