A steamer goes downstream from one port to another in 8 hours and same
distance upstream in 12 hours. If the speed of stream is 2 km/hr. Find speed of
steamer in still water and distance between ports.
Answers
Solution :
In the above questión , the following details are mentioned -
• A streamer goes downstream from one fort to another in 8 hours and can travel the same distance upstream in We hours .
• Speed of the stream is 2 km/hr .
We have to find the speed of the streamer in still water and the distance in the ports . Let us start by assigning these variables first. Suppose that the speed of the streamer in still water is x km/hr and the distance between the two ports is d km.
Speed = [ Distance/Time]
Time = [ distance/speed ]
Speed of the streamer upstream = ( x - 2) kmph
Speed of the streamer downstream = ( x + 2) kmph
Speed upstream = ( x - 2) = d/12
Speed downstream = (x+2) = d/8
Dividing the two equations with each other
> ( x-2)/(x+2) = 8/12 = 2/3
> 3x - 6 = 2x + 4
> x = 10 km/hr
D = 96 km .
Answer - The speed of the streamer in still water and the distance between the ports are 10kmph and 96 km respectively .
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Let the speed of the steamer be x
Given that the speed of the stream is 2 km/h
Find upstream distance:
steamer's upstream speed = (x - 2) km/h
Distance = Speed x times
Distance = (x - 2) x 15
Distance = 15(x -2)
Find downstream distance:
steamer's downstream speed = (x + 2) km/h
Distance = Speed x times
Distance = (x + 2) x 12
Distance = 12(x + 2)
Solve x:
Given that both upstream and downstream distance is the same.
15(x - 2) = 12(x + 2)
15x - 30 = 12x + 24
3x = 54
x = 18
The speed of the steamer in still water is 18 km/h
Find the distance:
Distance = 15(18 - 2) = 240 km
Answer: The speed of the steamer in still water is 18km/h and the distance is 240 km.