Expert: Abe Mantell - 5/22/2006

Question
Hello.  I m in pre-calc, and I have a question about a word problem that is driving me up a wall.  I know that you must combine inequalities in it somehow, but I just can t figure it out -- it almost seems like something is missing.  Normally I d be able to figure it out, but a new anti-siezure medication that I m on makes it difficult for me to concentrate and remember things, including equations as simple as 5+2, and how to spell simple words.  This obviously interferes with doing work, however my school is extremely uncooperative and I m just trying to get through the last few weeks before the end of the year, without damaging my GPA too much... until I can get my health issues resolved.  I also don t have a teacher to explain this to me (as I am out of the classroom).  Anyway, after trying for a few hours to get this one problem (I m persistant to say the least), I got 3.75 mph, but I know that this is incorrect.      Here s the problem:    A motorboat heads upstream on a river that has a current of  miles per hour.  The trip upstream takes 5 hours, while the return trip takes 2.5 hours.  Assuming that the motorboat maintains a constant speed relative to the water, what is the speed of the motorboat?    My work:    Upstream ... V (constant speed) = (v-3)     T(time) = 5  Downstream ... V = (v+3)   T = 5    2v = 7.5  7.5/2 = 3.75 mph    I know that I ve A) over-simplified, and B) left a step out, but I can t think of where it is.  This is how my brain works now -- in an overly simple manner.  I can t even begin to comprehend an additional step.    I d appreciate any help.  Thanks!

Answer
Hello Jax,

Sorry to hear of your health problem...good luck!

You left out some info, so I will assume certain things
(correct me if I am wrong).
1. The river has a current flow of 3 miles/hr
2. The speed of the boat is 'v'

Let x=the one-way distance
Hence, 5(v-3)=x AND 2.5(v+3)=x...thus, 5(v-3)=2.5(v+3)
==> 5v-15=2.5v+7.5 ==> 2.5v=22.5 ==> v=9 miles/hour

Abe