Difference between revisions of "2010 AMC 12B Problems/Problem 7"
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== Solution == | == Solution == | ||
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+ | Let <math>x</math> be the time it is not raining, and <math>y</math> be the time it is raining, in hours. | ||
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+ | We have the system: <math>30x+20y=16</math> and <math>x+y=2/3</math> | ||
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+ | Solving gives <math>x=\frac{4}{15}</math> and <math>y=\frac{2}{5}</math> | ||
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+ | We want <math>y</math> in minutes, <math>\frac{2}{5}*60=24 \Rightarrow C</math> | ||
== See also == | == See also == | ||
{{AMC12 box|year=2010|num-b=6|num-a=8|ab=B}} | {{AMC12 box|year=2010|num-b=6|num-a=8|ab=B}} |
Revision as of 19:20, 28 January 2011
Problem 7
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
Let be the time it is not raining, and be the time it is raining, in hours.
We have the system: and
Solving gives and
We want in minutes,
See also
2010 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
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 12 Problems and Solutions |