SOLUTION: A tugboat goes 120 miles upstream in 10 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without current and the speed of the current.

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Question 633053: A tugboat goes 120 miles upstream in 10 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without current and the speed 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
againstcurrent x-y 10 hours
with current x+y 5 hours

Distance = 120 miles distance= 120
t=d/r against current
120.00 / ( x - y )= 10.00

10.00 x - -10.00 y = 120.00 ....................1
downstream
120.00 / ( x + y )= 5.00
5.00 ( x + y ) = 120.00
5.00 x + 5.00 y = 120.00 ...............2
Multiply (1) by 1.00
Multiply (2) by 2.00
we get
10.00 x + -10.00 y = 120.00
10.00 x + 10.00 y = 240.00
20.00 x = 360.00
/ 20.00
x = 18 mph

plug value of x in (1)
10 x -10 y = 120
180 -10 y = 120
-10 y = 120 -180
-10 y = -60
y = 6 mph
Boat 18 mph
current 6 mph
m.ananth@hotmail.ca