Difference between revisions of "2018 AMC 8 Problems/Problem 12"
(→Problem 12) |
m (→Solution) |
||
| Line 5: | Line 5: | ||
== Solution == | == Solution == | ||
| − | We see that every <math>35</math> minutes the clock passes, the watch passes <math>30</math> minutes. That means that the clock is <math>\frac{7}{6}</math> as fast the watch, so when the car clock passes <math>7</math> hours, the watch has passed <math>6</math> hours, meaning that the time would be <math>\boxed{\textbf{(B) }6:00}</math> | + | We see that every <math>35</math> minutes the clock passes, the watch passes <math>30</math> minutes. That means that the clock is <math>\frac{7}{6}</math> as fast the watch, so we can set up proportions. |
| + | <math>\dfrac{\text{car clock}}{\text{watch}}=\dfrac{7}{6}=\dfrac{7 \text{hours}}{x \text{hours}}</math>. Cross-multiplying we get <math>x=6</math>. Now this is obviously redundant, we could just eyeball it and see that the watch would have passed <math>6</math> hours, but this method better when the numbers are a bit more complex, which makes it both easier and reliable. | ||
| + | |||
| + | --BakedPotato66 | ||
| + | |||
| + | Alternate Solution: When the car clock passes <math>7</math> hours, the watch has passed <math>6</math> hours, meaning that the time would be <math>\boxed{\textbf{(B) }6:00}</math> | ||
==See Also== | ==See Also== | ||
Revision as of 10:01, 17 August 2020
Problem 12
The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?
Solution
We see that every 
minutes the clock passes, the watch passes 
minutes. That means that the clock is 
as fast the watch, so we can set up proportions.
. Cross-multiplying we get 
. Now this is obviously redundant, we could just eyeball it and see that the watch would have passed 
hours, but this method better when the numbers are a bit more complex, which makes it both easier and reliable.
--BakedPotato66
Alternate Solution: When the car clock passes 
hours, the watch has passed hours, meaning that the time would be 
See Also
| 2018 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. 
