Question

Each day for four days, Linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. Each day after the first, her speed decreased so that the number of minutes to travel one mile increased by $5$ minutes over the preceding day. Each of the four days, her distance traveled was also an integer number of miles. What was the total number of miles for the four trips?

$10$

$15$

$25$

$50$

$82$

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Written solution:

Linda traveled for $60$ minutes every day. Since one mile was traveled in an integer amount of minutes each day, her minutes per mile every day must be a factor of $60.$ The factors of $60$ are $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30,$ and $60.$ The only sequence of four of these numbers that differ by $5$ are $5, 10, 15,$ and $20.$ For the four days, she traveled $\dfrac{60}{5} + \dfrac{60}{10} + \dfrac{60}{15} + \dfrac{60}{20} = 25$ miles.

Thus, C is the correct answer.

2017 AMC 8 Problem 23

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Problem 23 in Other Years