Question 213801
A boat can go 33 mph in still water.  It take as long to go 300 miles upstream as it does to go downstream  360 miles . How fast is the current?


Step 1.  Let v be the velocity of the current.


Step 2.  Speed of boat in still water is 33 mph.  Velocity going upstream is 33-v and velocity going downsteam is 33+v


Step 3.  Distance=Time*Velocity and Upstream time = Downstream time


Step 4.  Upstream time = Distance/Velocity=300/(33-v)


Step 5.  Downstream time = 360/(33+v)


Step 6.  Set expressions in Step 4 and 5 to be equal since time traveled upstream equals to time traveled downstream.  Then


{{{300/(33-v)=360/(33+v)}}}


Multiply by (33-v)(33+v) to both sides of equation to get rid of denominators.


{{{300(33+v)=360(33-v)}}}


Divide by 60 to both sides of equation


{{{5(33+v)=6(33-v)}}}


{{{165+5v=198-6v}}}


Add 6v-165 to both sides of equation


{{{11v=33}}}


Divide by 33 to both sides of equation


{{{v=3}}}


Step 5.  So velocity of current is 3 mph.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J