Difference between revisions of "2012 AMC 8 Problems/Problem 3"
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| − | On February 13 | + | ==Problem== |
| + | On February 13 ''The Oshkosh Northwester'' listed the length of daylight as 10 hours and 24 minutes, the sunrise was <math> 6:57\textsc{am} </math>, and the sunset as <math> 8:15\textsc{pm} </math>. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set? | ||
<math> \textbf{(A)}\hspace{.05in}5:10\textsc{pm}\quad\textbf{(B)}\hspace{.05in}5:21\textsc{pm}\quad\textbf{(C)}\hspace{.05in}5:41\textsc{pm}\quad\textbf{(D)}\hspace{.05in}5:57\textsc{pm}\quad\textbf{(E)}\hspace{.05in}6:03\textsc{pm} </math> | <math> \textbf{(A)}\hspace{.05in}5:10\textsc{pm}\quad\textbf{(B)}\hspace{.05in}5:21\textsc{pm}\quad\textbf{(C)}\hspace{.05in}5:41\textsc{pm}\quad\textbf{(D)}\hspace{.05in}5:57\textsc{pm}\quad\textbf{(E)}\hspace{.05in}6:03\textsc{pm} </math> | ||
| − | ==Solution== | + | ==Solution 1== |
The problem wants us to find the time of sunset and gives us the length of daylight and time of sunrise. So all we have to do is add the length of daylight to the time of sunrise to obtain the answer. Convert 10 hours and 24 minutes into <math>10:24</math> in order to add easier. | The problem wants us to find the time of sunset and gives us the length of daylight and time of sunrise. So all we have to do is add the length of daylight to the time of sunrise to obtain the answer. Convert 10 hours and 24 minutes into <math>10:24</math> in order to add easier. | ||
Adding, we find that the time of sunset is <math> 6:57\textsc{am} + 10:24 \implies 17:21 \implies \boxed{\textbf{(B)}\ 5:21\textsc{pm}}</math>. | Adding, we find that the time of sunset is <math> 6:57\textsc{am} + 10:24 \implies 17:21 \implies \boxed{\textbf{(B)}\ 5:21\textsc{pm}}</math>. | ||
| + | |||
| + | ==Solution 2 (Answer choices)== | ||
| + | The length of daylight is 10 hours and 24 minutes, but for now, we can just look at the 24 minutes. Add 24 minutes to 57 part of sunrise, and you see that the sunset time must end in a 21. We see that the only option that ends with 21 is <math>\implies \boxed{\textbf{(B)}\ 5:21\textsc{pm}}</math>. | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/v0SDWGo1_nU ~savannahsolver | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2012|num-b=2|num-a=4}} | {{AMC8 box|year=2012|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 20:18, 28 June 2022
Problem
On February 13 The Oshkosh Northwester listed the length of daylight as 10 hours and 24 minutes, the sunrise was 
, and the sunset as 
. The length of daylight and sunrise were correct, but the sunset was wrong. When did the sun really set?
Solution 1
The problem wants us to find the time of sunset and gives us the length of daylight and time of sunrise. So all we have to do is add the length of daylight to the time of sunrise to obtain the answer. Convert 10 hours and 24 minutes into 
in order to add easier.
Adding, we find that the time of sunset is 
.
Solution 2 (Answer choices)
The length of daylight is 10 hours and 24 minutes, but for now, we can just look at the 24 minutes. Add 24 minutes to 57 part of sunrise, and you see that the sunset time must end in a 21. We see that the only option that ends with 21 is 
.
Video Solution
https://youtu.be/v0SDWGo1_nU ~savannahsolver
See Also
| 2012 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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. 
