SOLUTION: The current in a stream moves at a speed of 3mph. A boat travels 45mi upstream and 45mi downstream in a total time of 8 hr. What is the speed of the boat in still water?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The current in a stream moves at a speed of 3mph. A boat travels 45mi upstream and 45mi downstream in a total time of 8 hr. What is the speed of the boat in still water?      Log On


   

Question 156479: The current in a stream moves at a speed of 3mph. A boat travels 45mi upstream and 45mi downstream in a total time of 8 hr. What is the speed of the boat in still water?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
let r=rate (speed) of boat in still water
time to travel upstream=45/(r-3)
time to travel downstream=45/(r+3)
And we are told that the above two times add up to 8 hours, so:
45/(r-3)+45/(r+3)=8 multiply each term by (r-3)(r+3)
45(r+3)+45(r-3)=8(r-3)(r+3) get rid of parens
45r+135+45r-135=8r^2-72 or
90r=8r^2-72 subtract 90r from each side
90r-90r=8r^2-90r-72 and
8r^2-90r-72=0 quadratic in standard form. Solve using the quadratic formula:
r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
r+=+%2890+%2B-+sqrt%28%28-90%5E2%29-4%2A8%2A%28-72%29+%29%29%2F%2816%29+
r+=+%2890+%2B-+sqrt%2810404%29%29%2F%2816%29+
r+=+%2890+%2B-+102%29%2F%2816%29+
r+=+%2890+%2B+102%29%2F%2816%29+
r+=+%28192%29%2F%2816%29+
r=12 mph-----------------------------------ans
and
r+=+%2890+-+102%29%2F%2816%29+
r=-12%2F16-------------------NO GOOD----IN THIS PROBLEM, SPEED IS POSITIVE
CK
45/(12-3)+45/(12+3)=8
45/9 +45/15=8
5+3=8
8=8

Hope this helps---ptaylor