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Difference between revisions of "2011 AMC 12A Problems/Problem 12"

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== Problem ==
 
== Problem ==
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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>?
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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 boat to go from <math>A</math> to <math>B</math>?
  
 
<math>
 
<math>

Revision as of 00:51, 7 January 2012

Problem

A power boat and a raft both left dock $A$ 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 $B$ downriver, then immediately turned and traveled back upriver. It eventually met the raft on the river 9 hours after leaving dock $A.$ How many hours did it take the power boat to go from $A$ to $B$?

$\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 3.5 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 4.5 \qquad \textbf{(E)}\ 5$

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 $0$. In this case, when the powerboat travels from $A$ to $B$, the raft remains at $A$. Thus the trip from $A$ to $B$ takes the same time as the trip from $B$ to the raft. Since these times are equal and sum to $9$ hours, the trip from $A$ to $B$ must take half this time, or $4.5$ hours. The answer is thus $\boxed{\textbf{D}}$.

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
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