SOLUTION: A boat on a river travels 24 miles downstream in only 3 hours. It takes the same boat 5 hours to travel 20 miles upstream. What are the speed of the boat and the speed of the curre

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Question 909352: A boat on a river travels 24 miles downstream in only 3 hours. It takes the same boat 5 hours to travel 20 miles upstream. What are the speed of the boat and the speed of the current?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
boat speed =x mph
current speed =y mph
against current 5 hours
with current 3 hours

Distance against 20 miles distance with 24 miles
t=d/r against current -
20.00 / ( x - y )= 5.00
5.00 ( x - y ) = 3.00
5.00 x - 5.00 y = 20.00 ....................1

24.00 / ( x + y )= 3.00
3.00 ( x + y ) = 24.00
3.00 x + 3.00 y = 24.00 ...............2
Multiply (1) by 3.00
Multiply (2) by 5.00
we get
15.00 x + -15.00 y = 60.00
15.00 x + 15.00 y = 120.00
30.00 x = 180.00
/ 30.00
x = 6.00 mph

plug value of x in (1) y
5.00 x -5.00 y = 20.00
30.00 -5.00 -30.00 = 20.00
-5.00 y = 20.00
-5.00 y = -10.00 mph
y = 2.00
boat speed 6.00 mph
current speed 2.00 mph

m.ananth@hotmail.ca