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Difference between revisions of "2004 AMC 8 Problems/Problem 12"

(Created page with "==Problem== 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 <math>24</math> hours. If she is using it ...")
 
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she is using it constantly, the battery will last for only <math>3</math> hours.
 
she is using it constantly, the battery will last for only <math>3</math> hours.
 
Since the last recharge, her phone has been on <math>9</math> hours, and during
 
Since the last recharge, her phone has been on <math>9</math> hours, and during
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that time she has used it for <math>60</math> minutes. If she doesn’t talk any
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that time she has used it for <math>60</math> minutes. If she doesn’t use it any
 
more but leaves the phone on, how many more hours will the battery last?
 
more but leaves the phone on, how many more hours will the battery last?
  
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==Solution==
 
==Solution==
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When not being used, the cell phone uses up <math>1/24</math> of its battery per hour. When being used, the cell phone uses up <math>1/3</math> of its battery per hour. Since Niki's phone has been on for <math>9</math> hours, of those <math>8</math> simply on and <math>1</math> being used to talk, <math>8(1/24) + 1(1/3) = 2/3</math> of its battery has been used up. To drain the remaining <math>1/3</math> the phone can last for <math>\frac{1/3}{1/24}=\boxed{\textbf{(B)}\ 8}</math> more hours without being used.
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When not being used, the cell phone uses up <math>\frac{1}{24}</math> of its battery per hour. When being used, the cell phone uses up <math>\frac{1}{3}</math> of its battery per hour. Since Niki's phone has been on for <math>9</math> hours, of those <math>8</math> simply on and <math>1</math> being used to talk, <math>8(\frac{1}{24}) + 1(\frac{1}{3}) = \frac{2}{3}</math> of its battery has been used up. To drain the remaining <math>\frac{1}{3}</math> the phone can last for <math>\frac{\frac{1}{3}}{\frac{1}{24}}=\boxed{\textbf{(B)}\ 8}</math> more hours without being used.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2004|num-b=11|num-a=13}}
 
{{AMC8 box|year=2004|num-b=11|num-a=13}}
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{{MAA Notice}}

Latest revision as of 13:28, 29 January 2023

Problem

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 use it any more but leaves the phone on, how many more hours will the battery last?

$\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 8 \qquad \textbf{(C)}\ 11 \qquad \textbf{(D)}\ 14 \qquad \textbf{(E)}\ 15$

Solution

When not being used, the cell phone uses up $\frac{1}{24}$ of its battery per hour. When being used, the cell phone uses up $\frac{1}{3}$ of its battery per hour. Since Niki's phone has been on for $9$ hours, of those $8$ simply on and $1$ being used to talk, $8(\frac{1}{24}) + 1(\frac{1}{3}) = \frac{2}{3}$ of its battery has been used up. To drain the remaining $\frac{1}{3}$ the phone can last for $\frac{\frac{1}{3}}{\frac{1}{24}}=\boxed{\textbf{(B)}\ 8}$ more hours without being used.

See Also

2004 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 11 		Followed by
Problem 13
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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