SOLUTION: a boat traveled 210 miles downstream and back. the trip downstream took 10 hours. the trip back took 70 hours. Find the speed of the boat in still water and the speed of the curren

Algebra ->  Equations -> SOLUTION: a boat traveled 210 miles downstream and back. the trip downstream took 10 hours. the trip back took 70 hours. Find the speed of the boat in still water and the speed of the curren      Log On


   

Question 206439: a boat traveled 210 miles downstream and back. the trip downstream took 10 hours. the trip back took 70 hours. Find the speed of the boat in still water and the speed of the current.
Answer by mickclns(59) About Me  (Show Source):
You can put this solution on YOUR website!
Let c be the speed of the current and b the speed of the boat in still water (we assume this speed is constant)
D=RT, distance = rate x time
the distance is 210 in each direction
the rate downstream (current pushing the boat forward) is b+c
the rate upstream (current dragging against the boat) is b-c
210 = (b+c) x 10 (downstream)
210 = (b-c) x 70 (upstream)
dividing both sides of top equation by 10 and bottom equation by 70 we have
21 = b+c
3 = b-c
adding the left & right sides of the top equation to L&R sides of bottom equation, we have
24 = 2b (eliminating c)
b = 12 and
c=9, since 3 = 12-c
So, the speed of the boat in still water is 12 mph and the speed of the current is 9 mph