SOLUTION: A crew rows 4 miles downstream and 2 miles upstream in one hour. Then it rows 6 miles downstream and 5 miles upstream in 2 hours. Find the rate of the stream and that of the crew i

Question 903384: A crew rows 4 miles downstream and 2 miles upstream in one hour. Then it rows 6 miles downstream and 5 miles upstream in 2 hours. Find the rate of the stream and that of the crew in still water
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let speed with current = x
speed against current be y
t=d/r
time downstream + time upstream = total time
4/x +2/y = 1
let 1/x =a and 1/y be y
4a+2b=1.........................(1)
6/x +5/y =2
6a+5b=2.........................(2)
4 a + 2 b = 1 .............1

6 a + 5 b = 2 .............2
Eliminate y
multiply (1)by -5
Multiply (2) by 2
-20 a -10 b = -5
12 a + 10 b = 4
Add the two equations
-8 a = -1
/ -8
a = 0.125
x=1/a=1/0.125= 8
speed of boat = 8 mph
plug value of a in (1)
4 a + 2 b = 1
1 + 2 b = 1
2 b = 1 -1
2 b = 1
b = 0.25
b=0.25 y=1/b =1/0.25= 4
speed of current = 4 mph

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