Jasmine's pace for a 3-mile race is 1 minute per mile faster than her pace for a 13-mile race. She ran the 3-mile race in 21 minutes. How many minutes will it take her to run the 13-mile race?
Jasmine will take 104 minutes to run the 13-mile race.
Jasmine's pace for the 3-mile race is 7 minutes per mile, and since she is 1 minute faster per mile than her pace for the 13-mile race, her pace for the longer race must be 8 minutes per mile. Therefore, multiplying her 13-mile distance by this pace yields a total time of 104 minutes.
This option suggests an unrealistically fast pace, implying that Jasmine would run each mile of the 13-mile race in only 2.62 minutes. This is much faster than any feasible human running speed, especially considering her established pace for the shorter race.
Selecting 78 minutes indicates a pace of approximately 6 minutes per mile for the 13-mile race. This is contradictory to the information given that her pace for the longer race is actually slower than her pace for the shorter race, making this option incorrect.
A time of 92 minutes translates to a pace of about 7.08 minutes per mile for the 13-mile race. While this is a possibility, it still does not account for the fact that she runs the shorter race at a faster pace and should have a slower pace for the longer race, thus making this choice incorrect.
If Jasmine took 101 minutes, her pace would be approximately 7.77 minutes per mile. Although this is slower than her pace for the 3-mile race, it does not align with the requirement that her pace for the 13-mile race is 1 minute slower than that pace, which must be 8 minutes per mile.
The calculations confirm that Jasmine's time for the 13-mile race is 104 minutes, based on her established pace for the shorter race. This logical deduction punctuates the relationship between her race times and validates the conclusion that her slower pace for the longer distance results in a total time that matches the correct answer.
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