SOLUTION: A motorboat traveling upstream went 30 miles in 1.5 hours. Going downstream, it took only 1 hour to travel the same distance. Find the rate of the boat in calm water and the rat

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Question 866166: A motorboat traveling upstream went 30 miles in 1.5 hours. Going downstream, it took only 1 hour to travel the same distance. Find the rate of the boat in calm water and the rate of the current.
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
boat speed =x mph
current speed =y mph
against current 1.5 hours
with current 1 hours

Distance against 30 miles distance with 30 miles
t=d/r against current -
30.00 / ( x - y )= 1.50
1.50 ( x - y ) = 1.00
1.50 x - 1.50 y = 30.00 ....................1

30.00 / ( x + y )= 1.00
1.00 ( x + y ) = 30.00
1.00 x + 1.00 y = 30.00 ...............2
Multiply (1) by 1.00
Multiply (2) by 1.50
we get
1.50 x + -1.50 y = 30.00
1.50 x + 1.50 y = 45.00
3.00 x = 75.00
/ 3.00
x = 25.00 mph

plug value of x in (1) y
1.50 x -1.50 y = 30.00
37.50 -1.50 -37.50 = 30.00
-1.50 y = 30.00
-1.50 y = -7.50 mph
y = 5.00
boat speed 25.00 mph
current speed 5.00 mph

m.ananth@hotmail.ca