SOLUTION: A sailboat travels 20 miles downstream in three hours. It returns in four hours. Find the speed of the sailboat in still water AND the rate of the current.

Algebra ->  Average -> SOLUTION: A sailboat travels 20 miles downstream in three hours. It returns in four hours. Find the speed of the sailboat in still water AND the rate of the current.      Log On


   

Question 183638This question is from textbook Algebra
: A sailboat travels 20 miles downstream in three hours. It returns in four hours. Find the speed of the sailboat in still water AND the rate of the current. This question is from textbook Algebra

Answer by halbren(10) About Me  (Show Source):
You can put this solution on YOUR website!
This is a speed and distance problem. The assumption here is the speed of the sailboat is the same in both direction. The current however will help travel downstream and low travel upstream. The distance travelled in each direction will be the same.
d=s%2At+%2B+c%2At where s=speed of sailboat and c=speed of current
downstream would be
20+=+s%2A3+%2B+c%2A3
coming back upstream
20+=+s%2A4+-+c%2A4
If we solve the second equation for s we get
20+%2B+4c+=+4s
Divide both sides by 4
20%2F4+%2B+4c%2F4+=+4s%2F4
Simplify
5%2Bc=s
Using substitution, replace s with 5+c in first equation
20+=+3%285%2Bc%29%2B3c
Distribute to remove parenthesis
20=15%2B3c%2B3c
Move constants to one side and combined like variables
20-15=6c
5=6c
divide both sides by 6
5%2F6=6c%2F6
c=5%2F6mph
Put this value for c back into s=5+c
s=5%2B5%2F6mph