Difference between revisions of "2010 AMC 10B Problems/Problem 10"
(Created page with 'We know that <math>d = vt</math> Since we know that she drove both when it was raining and when it was not and that her total distance traveled is <math>16</math> miles. We als…') |
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| + | ==Problem== | ||
| + | Shelby drives her scooter at a speed of <math>30</math> miles per hour if it is not raining, and <math>20</math> miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of <math>16</math> miles in <math>40</math> minutes. How many minutes did she drive in the rain? | ||
| + | |||
| + | <math>\textbf{(A)}\ 18 \qquad \textbf{(B)}\ 21 \qquad \textbf{(C)}\ 24 \qquad \textbf{(D)}\ 27 \qquad \textbf{(E)}\ 30</math> | ||
| + | |||
| + | ==Solution== | ||
We know that <math>d = vt</math> | We know that <math>d = vt</math> | ||
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We know now that the time traveled in rain was <math>\dfrac{2}{5}</math> of an hour, which is <math>\dfrac{2}{5}*60 = 24</math> minutes | We know now that the time traveled in rain was <math>\dfrac{2}{5}</math> of an hour, which is <math>\dfrac{2}{5}*60 = 24</math> minutes | ||
| − | So, our answer is | + | So, our answer is <math> \boxed{\textbf{(C)}\ 24} </math> |
| − | + | ==See Also== | |
| + | {{AMC10 box|year=2010|ab=B|num-b=9|num-a=11}} | ||
Revision as of 00:54, 26 November 2011
Problem
Shelby drives her scooter at a speed of 
miles per hour if it is not raining, and 
miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of 
miles in 
minutes. How many minutes did she drive in the rain?
Solution
We know that 
Since we know that she drove both when it was raining and when it was not and that her total distance traveled is miles.
We also know that she drove a total of minutes which is 
of an hour.
We get the following system of equations, where 
is the time traveled when it was not raining and 
is the time traveled when it was raining:
Solving the above equations by multiplying the second equation by 30 and subtracting the second equation from the first we get:
We know now that the time traveled in rain was 
of an hour, which is 
minutes
So, our answer is 
See Also
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 AMC 10 Problems and Solutions | ||
