SOLUTION: A tugboat goes 120 miles upstream in 15 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without a current and the speed of the current.

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Question 671719: A tugboat goes 120 miles upstream in 15 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without a current 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
againstcurrent x-y 15 hours
with current x+y 5 hours

Distance = 120 miles distance= 120
t=d/r against current -
120.00 / ( x y )= 15.00
y
15.00 x - -15.00 = 120.00 ....................1
downstream +
120.00 / ( x y y )= 5.00
5.00 ( x + y ) = 120.00
5.00 x + 5.00 = 120.00 ...............2
Multiply (1) by 1.00
Multiply (2) by 3.00
we get y
15.00 x + -15.00 y = 120.00
15.00 x + 15.00 = 360.00
30.00 x = 480.00
/ 30.00
x = 16 mph

plug value of x in (1) y
15 x -15 y = 120
240 -15 -240 = 120
-15 y = 120
-15 y = -120 mph
y = 8
Boat 16 mph
current 8 mph