# Hard math question?

<p>This is from AMC 2011. </p>

<p>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 raft to go from A to B?</p>

<p>A)3 B)3.5 C)4 D)4.5 E)5</p>

<p>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 D.</p>

<p>Source: 2011</a> AMC 12A Problems/Problem 12 - AoPSWiki</p>

<p>Yeah I read that explanation but didn't quite understand it however I get it now. Thanks.</p>

<p>This question prevented me from qualifying for the AIME... I still can't believe it...</p>