AMC8 2004

AMC8 2004 · Q12

AMC8 2004 · Q12. It mainly tests Rates (speed).

Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for 24 hours. If she is using it constantly, the battery will last for only 3 hours. Since the last recharge, her phone has been on 9 hours, and during that time she has used it for 60 minutes. If she doesn't talk any more but leaves the phone on, how many more hours will the battery last?

Niki 通常保持她的手机开着。如果她的手机开着但她没有实际使用它，电池能持续 24 小时。如果她持续使用它，电池只能持续 3 小时。自上次充电以来，她的手机已经开机 9 小时，在此期间她使用了 60 分钟。如果她不再通话但保持手机开着，电池还能持续多少小时？

(A) 7 7

(B) 8 8

(D) 14 14

(E) 15 15

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) The phone has been used for 60 minutes, or 1 hour, to talk, during which time it has used $\frac{1}{3}$ of the battery. In addition, the phone has been on for 8 hours without talking, which used an additional $\frac{8}{24}$ or $\frac{1}{3}$ of the battery. Consequently, $\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$ of the battery has been used, meaning that $\frac{1}{3}$ of the battery, or $\frac{1}{3}\times 24=8$ hours remain if Niki does not talk on her phone.

（B）手机已通话60分钟，即1小时，在此期间消耗了电量的$\frac{1}{3}$。此外，手机在不通话的情况下开机了8小时，又额外消耗了$\frac{8}{24}$，即电量的$\frac{1}{3}$。因此，$\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$的电量已经被消耗，这意味着还剩下$\frac{1}{3}$的电量；如果Niki不再用手机通话，则剩余时间为$\frac{1}{3}\times 24=8$小时。

Topics

AR.007 Rates (speed)