AMC 8 2002 Problem 18
AMC8 2002 年第 18 题
方程与不等式★★★☆☆
Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day for 3 days. How long would he have to skate the ninth day in order to average 85 minutes of skating each day for the entire time?
Gage 连续 5 天每天滑冰 1 小时 15 分钟，连续 3 天每天滑冰 1 小时 30 分钟。那么第九天他需要滑多长时间才能使得在全部时间内每天平均滑 85 分钟？
- A.
- B. / 1 小时 10 分钟
- C. / 1 小时 20 分钟
- D. / 1 小时 40 分钟
- E.
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Converting into minutes and adding, we get that she skated 75*5+90*3+x = 375+270+x = 645+x minutes total, where is the amount she skated on day 9. Dividing by 9 to get the average, we get . Solving for , 645+x=765 x=120 Now we convert back into hours and minutes to get .
For the first five days, each day you are 10 minutes short of 85 minutes. And for the next three days, you are 5 minutes above 85 minutes. So in total you are missing 3*5-5*10, which equals to negative 35. So on the ninth day, to have an average of 85 minutes, Gage need to skate for 85+35 minutes, which is 120 minutes, or .
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