SOLUTION: a boat is rowed up stream 40 km and downstream 45 km in 13 hour . it also rowed up stream 30 km and downstream 27 km in 9 hour. find the speed of the boat and that of the stream.

Question 718095: a boat is rowed up stream 40 km and downstream 45 km in 13 hour . it also rowed up stream 30 km and downstream 27 km in 9 hour. find the speed of the boat and that of the stream.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
speed upstream = x
speed downstream = y
time = distance/time
Time upstream + time down stream = 13 hours
40/x +45/y = 13
let 1/x =a and 1/y =b
40a+45b =13................(1)
Similarly
30/x +27/y 9
30a+27b=9..................(2)

40 a + 45 b = 13 .............1
Total value
30 a + 27 b = 9 .............2
Eliminate y
multiply (1)by -3
Multiply (2) by 5
-120 a -135 b = -39
150 a + 135 b = 45
Add the two equations
30 a = 6
/ 30
a = 1/ 5
plug value of a in (1)
40 a + 45 b = 13
8 + 45 b = 13
45 b = 13 -8
45 b = 5
b = 1/ 9
a= 1/ 5
therefore x=5 speed upstream
b= 1/ 9
y=9 speed downstream
so speed of boat = 7 km/h
speed of current = 2 km/h

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