The Hudson River flows at a rate of 5 miles per hour A patro

The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=speed of the boat in still water
r-5=patrol boat\'s rate upstream (against the current)
and r+5=patrol boat\'s rate downstream (with the current)
Time travelling upstream =40/(r-5)
Time travelling downstream=40/(r+5)
And we are told that the above times add up to 6 hr
So:
40/(r-5) + 40/(r+5)=6 multiply each term by (r-5)(r+5)
40(r+5)+40(r-5)=6(r+5)(r-5) get rid of parens
40r+200+40r-200=6r^2-150 simplify
80r=6r^2-150 divide each term by 2
40r=3r^2-75 subtract 40r from each side
3r^2-40r-75=0 quadratic in standard form and it can be factored:
(3r+5)(r-15)=0
r=15--------------------------answer
and
r=-5/3-----------------disregard negative value for rate---in this problem, rate is positive
CK
40/10 +40/20=6
4+2=6
6=6