SOLUTION: hi can someone help me with this.. A man can row 12 miles upstream in a river and back in 7 1/2 hours. He can row 1 mile upstream in th same time that he can row 4 miles downstr

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Question 511374: hi can someone help me with this..
A man can row 12 miles upstream in a river and back in 7 1/2 hours. He can row 1 mile upstream in th same time that he can row 4 miles downstream. Find the speed of the boat in still water and the speed of the current.
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
A man can row 12 miles upstream in a river and back in 7 1/2 hours. He can row 1 mile upstream in th same time that he can row 4 miles downstream. Find the speed of the boat in still water and the speed of the current.
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2 conditions given, so use 2 equations to solve:
let x=speed of boat in still water
let c=speed of current
x+c =speed of boat downstream
x-c = speed of boat upstream
..
Travel time=distance/speed
1/(x-c)=4/(x+c)
x+c=4x-4c
5c=3x
c=3x/5
..
12/(x-c)+12/(x+c)=7.5
LCD:(x+c)(x-c)
12x+12c+12x-12c=7.5(x+c)(x-c)
24x=7.5(x^2-c^2) (difference of squares)
24x=7.5(x^2-(3x/5)^2)=7.5(x^2-9x^2/25)=7.5[(25x^2-9x^2)/25]
24x=7.5[16x^2/25]=(7.5/25)(16x^2)=.3(16x^2)=4.8x^2
4.8x^2-24x=0
x(4.8x-24=0
x=0 (reject, speed>0)
4.8x-24=0
x=24/4.8=5 mph
c=3x/5=15/5=3mph
ans:
speed of boat in still water=5 mph
speed of current=3 mph