a steamer is going downstream in a river cover distance between two ports in 12 hrs . coming back upstream , it covers this distance in 18 hrs . the speed of water is 4 km/hr . find the speed of boat
Answers
Solution :
Let us assume that the speed of the boat is x km/hr .
Now , the speed of the water is 4 km/hr .
Speed of the boat upstream :
> ( x - 4) km/hr
Speed of the boat downstream :
> ( x + 4) km/hr
Let the distance be s km .
The streamer going downstream covers the distance in 12 hours.
The streamer going upstream covers the distance in 18 hours.
Speed = [ Distance ]/[ Time ]
> Speed downstream :
> s/12 .
> Speed Upstream :
> s/18 .
s/12 = ( x + 4)
s/18 = ( x - 4)
Dividing the equations.
> s/12 × 18/s = (x + 4)/(x - 4)
> 9/6 = ( x + 4)/(x - 4)
> 6( x + 4) = 9( x - 4)
> 6x + 24 = 9x - 36
> 3x = 60
> x = 20 .
Thus , the speed of the boat is 20 km/hr .
This is the required answer.
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Answer:
Given :-
a steamer is going downstream in a river cover distance between two ports in 12 hrs . coming back upstream , it covers this distance in 18 hrs . the speed of water is 4 km/hr
To Find :-
Speed of boat
Solution :-
Let the speed of boat be x km/hr
Now
When come upstream
x - 4 km/hr
When come downstream
x + 4 km/hr
Time to go downstream = 12 hr
Time to come upstream = 18 hr
Now,
S = D/T
S is the Speed
D is the Distance
T is the Time
Downstream = s/12 = (x + 4)
Upstream = s/18 = (x - 4)
s/18 × 12/s = (x + 4)/(x - 4)
18/12 = (x + 4)/(x - 4)
9/6 = (x + 4)/(x - 4)
6(x + 4) = 9(x - 4)
6x + 24 = 9x - 36
9x - 6x = 36 + 24
3x = 60
x = 20
Speed = 20 km/h