SOLUTION: Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream      Log On


   

Question 132538: Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key to these kind of problems is to spot
the thing that doesn't change in the different
instances given. In this case it's distance.
d+=+r%2At
(rate going upstream) = (rate of boat in still water - rate of stream)
(rate going downstream) = (rate of boat in still water + rate of stream)
The combined time for both trips is 3 hours. This is
separated into t anf 3+-+t
12+=+%289+%2B+s%29%2At (downstream)
12+=+%289+-+s%29%2A%283+-+t%29 (upstream)
t+=+12+%2F+%289+%2B+s%29
12+=+27+-+3s+-+9t+%2B+st
These are 2 equations and 2 unknowns, so should be solvable
12+=+27+-+3s+-+9%2A%2812%2F%289+%2B+s%29%29+%2B+s%2A%2812+%2F+%289+%2B+s%29%29
multiply both sides by 9+%2B+s
12%2A%289+%2B+s%29+=+27%2A%289+%2B+s%29+-+3s%2A%289+%2B+s%29+-+108+%2B+12s
108+%2B+12s+=+243+%2B+27s+-+27s+-+3s%5E2+-+108+%2B+12s
3s%5E2+%2B+216+-+243+=+0
3s%5E2+-+27+=+0
3s%5E2+=+27
s%5E2+=+9
s+=+3
The rate of the stream is 3 km/hr
check:
12+=+%289+%2B+s%29%2At (downstream)
12+=+%289+%2B+3%29%2At
12+=+12%2At
t+=+1
12+=+%289+-+s%29%2A%283+-+t%29 (upstream)
12+=+%289+-+3%29%2A%283+-+1%29
12+=+6%2A2
12+=+12
OK