Difference between revisions of "2010 AMC 10B Problems/Problem 10"
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==Solution 1== | ==Solution 1== | ||
| − | We know that <math>d = | + | We know that <math>d = rt</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. | 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. | ||
Revision as of 15:58, 5 January 2020
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 .
Solution 3
Shelby's overall speed is 
miles per hour. Since 
is 
as close to as it is from , Shelby spent 
as much time in the rain as she did in the sun, or 
of the total time. 
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
