Difference between revisions of "2010 AMC 10B Problems/Problem 10"
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==Solution 2== | ==Solution 2== | ||
− | We let <math>t</math> be the time Shelby drives in the rain. This gives us the equation <math> 20t + 30(\frac{2}{3} - t) = 16</math>. Expanding and rearranging gives us <math>10t = 4</math>, or <math>t = 0.4</math> hours. we multiply <math>0.4</math> by <math>60</math>, which gives us <math> \boxed{\textbf{(C)}\ 24} </math>. | + | We let <math>t</math> be the time Shelby drives in the rain. This gives us the equation <math> 20t + 30\left(\frac{2}{3} - t \right ) = 16</math>. Expanding and rearranging gives us <math>10t = 4</math>, or <math>t = 0.4</math> hours. we multiply <math>0.4</math> by <math>60</math>, which gives us <math> \boxed{\textbf{(C)}\ 24} </math>. |
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==See Also== | ==See Also== | ||
{{AMC10 box|year=2010|ab=B|num-b=9|num-a=11}} | {{AMC10 box|year=2010|ab=B|num-b=9|num-a=11}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 02:22, 5 January 2018
Contents
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 1
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
Solution 2
We let be the time Shelby drives in the rain. This gives us the equation . Expanding and rearranging gives us , or hours. we multiply by , which gives us .
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 |
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