SOLUTION: A boat covers 30km upstream and 22 km downstrean in 8 hours. Also,it takes 4 more hours to travel 40 km upstream and 44 km downstrean. Find the speed of the boat in still water an

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Question 752609: A boat covers 30km upstream and 22 km downstrean in 8 hours. Also,it takes 4 more hours to travel 40 km upstream and 44 km downstrean. Find the speed of the boat in still water and that of the stream.
Answer by dkppathak(439) (Show Source):
You can put this solution on YOUR website!
let speed of boat in still water is x km /h
and speed of current of water is y km/h
speed up stream =x-y km/h
speed of down stream =x+y km/h
speed =distance / time
or
time =distance/ speed
t1=30/x-y
t2 =22/x+y
as per given conditions
t1 +t2 =8
30/x-y +22/x+y =8 (i)
similarly
40/x-y +44/x+y =12 (ii)
let x-y =u
x+y =v
we can rewrite equation as
30/u +22/v = 8 (iii)
40/u +44/v = 12 (iv)
by solving equations by elimination method
we can solve U =5
and V=11
by substitute the value of u and v
we can rewrite equations as
x-y =5
x +y =11
by solving these equations
we can get
x=8 km/h
y=3 km/h
ANSWER speed of boat in still water is 8km/h
and speed of current of water is 3 km/h