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Question
While preparing to run a marathon, Amelia created a training schedule in which the distance of her longest run every week increased by a constant amount. If Amelia's training schedule requires that her longest run in week 4 is a distance of 8 miles and her longest run in week 16 is a distance of 26 miles, which of the following best describes how the distance Amelia runs changes between week 4 and week 16 of her training schedule?
While preparing to run a marathon, Amelia created a training schedule in which the distance of her longest run every week increased by a constant amount. If Amelia's training schedule requires that her longest run in week 4 is a distance of 8 miles and her longest run in week 16 is a distance of 26 miles, which of the following best describes how the distance Amelia runs changes between week 4 and week 16 of her training schedule?
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Solution
The correct option is D Amelia increases the distance of her longest run by 1.5 miles each week.
In Amelia’s training schedule, her longest run in week 16 will be 26 miles and her longest run in week 4 will be 8 miles. Thus, Amelia increases the distance of her longest run by 18 miles over the course of 12 weeks. Since Amelia increases the distance of her longest run each week by a constant amount, the amount she increases the distance of her longest run each week is
26−816−4=1812=32=1.5
The fraction whose numerator is 26 minus 8, and whose denominator is 16 minus 4, equals the fraction 18 over 12, which equals the fraction 3 over 2, which equals 1.5 miles.
Choices A, B, and C are incorrect because none of these training schedules would result in increasing Amelia’s longest run from 8 miles in week 4 to 26 miles in week 16. For example, choice A is incorrect because if Amelia increases the distance of her longest run by 0.5 miles each week and has her longest run of 8 miles in week 4, her longest run in week 16 would be 8 plus 0.5 times 12, equals 14 miles, not 26 miles.
Hence, Amelia increases the distance of her longest run by 1.5 miles each week.
In Amelia’s training schedule, her longest run in week 16 will be 26 miles and her longest run in week 4 will be 8 miles. Thus, Amelia increases the distance of her longest run by 18 miles over the course of 12 weeks. Since Amelia increases the distance of her longest run each week by a constant amount, the amount she increases the distance of her longest run each week is
26−816−4=1812=32=1.5
The fraction whose numerator is 26 minus 8, and whose denominator is 16 minus 4, equals the fraction 18 over 12, which equals the fraction 3 over 2, which equals 1.5 miles.
Choices A, B, and C are incorrect because none of these training schedules would result in increasing Amelia’s longest run from 8 miles in week 4 to 26 miles in week 16. For example, choice A is incorrect because if Amelia increases the distance of her longest run by 0.5 miles each week and has her longest run of 8 miles in week 4, her longest run in week 16 would be 8 plus 0.5 times 12, equals 14 miles, not 26 miles.
Hence, Amelia increases the distance of her longest run by 1.5 miles each week.
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