Difference between revisions of "2010 AMC 12B Problems/Problem 7"
Coolmath2017 (talk | contribs) (→Solution 2) |
Coolmath2017 (talk | contribs) (→Solution 2) |
||
Line 20: | Line 20: | ||
Thus, we have the equation, <math>\frac{1}{2}</math> * x + <math>\frac{1}{3}</math> * (40-x) = 16 | Thus, we have the equation, <math>\frac{1}{2}</math> * x + <math>\frac{1}{3}</math> * (40-x) = 16 | ||
− | Solving, gives <math>x</math>=16, so the amount of time it is not raining is <math>40</math>-<math>16</math>=<math>24</math> | + | Solving, gives <math>x</math> = 16, so the amount of time it is not raining is <math>40</math>-<math>16</math> = <math>24</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}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 13:26, 25 April 2020
Contents
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 1
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,
Solution 2
Let be the time it is raining. Thus, the number of minutes it is not raining is .
Since we are calculating the time in minutes, it is best to convert the speeds in minutes. Thus, the speed per minute when it is not raining is per minute, and per minute when it is not raining. Thus, we have the equation, * x + * (40-x) = 16
Solving, gives = 16, so the amount of time it is not raining is - =
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.