Tuesday, November 19, 2013

take me to the river

Humanity hates word problems.  But the reality is, once you know how to do a particular type of problem, it becomes easy.  This particular problem caused a real stir in my classes.  Post your solutions in the comments and I'll follow up with an answer...

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 dock A to dock B. 

1 comment:

  1. So a solution. There's a lot of things we don't know... the distance between the docks, the speed of the river... so it has to be true that those things can be any possible value and the problem will yield the same answer. So the key to success is to make the problem as simple as possible and calculate the solution. Consider the river. You have no idea how fast it flows, so pretend it's not moving at all. OK, I know that means it's not a river, but for this problem, let's pretend it's still. This means the raft never moves and the boat goes down and back in 9 hours, 4.5 hours each way. In fact, no matter how fast the river flows, the distance traveled by the boat plus the distance traveled by the raft is a total of down and back, one round trip. If this total remains constant, than each half has to take half the time and the boat trip takes 4.5 hours from dock A to dock B. Any current in the river would slow down the boat on the return trip, but the raft would meet the boat part way down the river.