SOLUTION: a tugboat goes 100 miles upstream in 10 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 740273: a tugboat goes 100 miles upstream in 10 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) (Show Source):
You can put this solution on YOUR website!
tugboat speed =x mph
current speed =y mph
against current 10 hours
with current 5 hours

Distance against 100 miles distance with 100 miles
t=d/r against current -
100 / ( x - y )= 10
10 ( x - y ) = 100
10 x - 10 y = 100 ....................1

100 / ( x + y )= 5
5 ( x + y ) = 100
5 x + 5 y = 100 ...............2
Multiply (1) by 1
Multiply (2) by 2 10
we get
10 x + -10 y = 100
10 x + 10 y = 200
20 x = 300
/ 20
x = 15.00 mph

plug value of x in (1) y
10 x -10 y = 100
150 -10 -150 = 100
-10 y = 100
-10 y = -50 mph
y = 5.00
tugboat speed 15.00 mph 100
current speed 5.00 mph 100

m.ananth@hotmail.ca