Difference between revisions of "2011 AMC 12A Problems/Problem 12"
(→Problem) |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | A power boat and a raft both left dock <math>A</math> on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock <math>B</math> downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock <math>A.</math> How many hours did it take the power raft to go from <math>A</math> to <math>B | + | A power boat and a raft both left dock <math>A</math> on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock <math>B</math> downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock <math>A.</math> How many hours did it take the power raft to go from <math>A</math> to <math>B</math>? |
<math> | <math> | ||
| Line 10: | Line 10: | ||
== Solution == | == Solution == | ||
| + | Since the speed of the river is not specified, the outcome of the problem must be independent of this speed. We may thus trivially assume that the river has a speed of <math>0</math>. In this case, when the powerboat travels from <math>A</math> to <math>B</math>, the raft remains at <math>A</math>. Thus the trip from <math>A</math> to <math>B</math> takes the same time as the trip from <math>B</math> to the raft. Since these times are equal and sum to <math>9</math> hours, the trip from <math>A</math> to <math>B</math> must take half this time, or <math>4.5</math> hours. The answer is thus <math>\boxed{\textbf{D}}</math> | ||
| + | |||
== See also == | == See also == | ||
{{AMC12 box|year=2011|num-b=11|num-a=13|ab=A}} | {{AMC12 box|year=2011|num-b=11|num-a=13|ab=A}} | ||
Revision as of 19:27, 10 February 2011
Problem
A power boat and a raft both left dock 
on a river and headed downstream. The raft drifted at the speed of the river current. The power boat maintained a constant speed with respect to the river. The power boat reached dock 
downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock 
How many hours did it take the power raft to go from to ?
Solution
Since the speed of the river is not specified, the outcome of the problem must be independent of this speed. We may thus trivially assume that the river has a speed of 
. In this case, when the powerboat travels from to , the raft remains at . Thus the trip from to takes the same time as the trip from to the raft. Since these times are equal and sum to 
hours, the trip from to must take half this time, or 
hours. The answer is thus 
See also
| 2011 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 11 |
Followed by Problem 13 |
| 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 | |
