SOLUTION: A motorboat travels 300 mi in 6 hours going upstream. It travels 456 mi going downstream in the same amount of time. What is the rate of the boat in still water and what is the rat

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Question 874839: A motorboat travels 300 mi in 6 hours going upstream. It travels 456 mi going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
300 / ( x - y )= 6
6 ( x - y ) = 4
6 x - 6 y = 300 ....................1

456 / ( x + y )= 4
4 ( x + y ) = 456
4 x + 4 y = 456 ...............2
Multiply (1) by 2
Multiply (2) by 3
we get
12 x + -12 y = 600
12 x + 12 y = 1,368
24 x = 1,968
/ 24
x = 82 mph

plug value of x in (1) y
6 x -6 y = 300
492 -6 -492 = 300
-6 y = 300
-6 y = -192 mph
y = 32
boat speed 82 mph
current speed 32 mph