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