a steamer travels 30 km upstream in the same duration of time it takes to travel 60 km down stream in the same river .if the speed of the river is 4km /hr , find the speed of the steamer in the still water
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Answer:
Let the speed of the boat in still water be ‘x’ km/hr. Now, as the boat is moving in water so it's relative velocity w.r.t the water will be considered for calculation. Therefore, given the speed of the river is 4 km/hr, then:
Relative velocity of boat going upstream = (Speed of boat) + (– Speed of river)
Since, the boat is going in opposite direction to the movement of water and velocity being a directional quantity therefore, a ‘-ve’ sign is taken.
⇒V(upstream) = x + (–4) = x – 4 km/hr.
Similarly, relative velocity of boat going downstream = Speed of boat + Speed of river
⇒ V(downstream) = x + 4 km/hr.
Now, as the time taken is same so one can write it as:
Time taken in going upstream = Time taken in going downstream
⇒(Displacement/Velocity going upstream) = (Displacement/Velocity going downstream)
Since, Velocity = (Displacement/Time)
⇒[30/(x−4)]=[60/(x+4)]
⇒(x+4)/(x−4)=60/30
⇒(x+4)=2∗(x−4)
⇒(x+4)=2x−8
⇒4+8=2x−x
⇒x=12km/hr.
So, the speed of the boat in still water = x = 12 km/hr.
Hence, solved ✌️.
Thanks .
Answer:
hi
Let the speed of the boat in still water be ‘x’ km/hr. Now, as the boat is moving in water so it's relative velocity w.r.t the water will be considered for calculation. Therefore, given the speed of the river is 4 km/hr, then:
Relative velocity of boat going upstream = (Speed of boat) + (– Speed of river)
Since, the boat is going in opposite direction to the movement of water and velocity being a directional quantity therefore, a ‘-ve’ sign is taken.
⇒V(upstream) = x + (–4) = x – 4 km/hr.
Similarly, relative velocity of boat going downstream = Speed of boat + Speed of river
⇒ V(downstream) = x + 4 km/hr.
Now, as the time taken is same so one can write it as:
Time taken in going upstream = Time taken in going downstream
⇒(Displacement/Velocity going upstream) = (Displacement/Velocity going downstream)
Since, Velocity = (Displacement/Time)
⇒[30/(x−4)]=[60/(x+4)]
⇒(x+4)/(x−4)=60/30
⇒(x+4)=2∗(x−4)
⇒(x+4)=2x−8
⇒4+8=2x−x
⇒x=12km/hr.
So, the speed of the boat in still water = x = 12 km/hr.
Step-by-step explanation:
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