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 distan ce traveled was also an integer number of miles. What was the total number of miles for the four trips?

A. 10

B. 15

C. 25

D. 50

E. 82

1. 2017 AMC 8 官方解析

翻译：连续四天，琳达以一定的速度行走一个小时结果她在整数分钟内走了一英里．在第一天之后的每一天，她的速度都在下降，所以每英里的行驶时间比前一天都增加了 5分钟．在这四天里，她所走的路程也是整数英里．求四天的总里程是（ ）？

设第一天$x$分走了一英里，于是列表如下：

$S_1 = 1 \div \frac{x}{60} \times 1 = \frac{60}{x}$，$S_2 = 1 \div \frac{x+5}{60} \times 1 = \frac{60}{x+5}$，$S_3 = 1 \div \frac{x+10}{60} \times 1 = \frac{60}{x+10}$，
$S_4 = 1 \div \frac{x+15}{60} \times 1 = \frac{60}{x+15}$，$S_1, S_2, S_3, S_4$都是整数，$x$只能是5，于是$S_1 = 12$，$S_2 = 6$，$S_3 = 4$，$S_4 = 3$，四天共走了12 + 6 + 4 + 3 = 25．