15. A boat travels 30 km upstream in the same amount of time it takes to travel 60 km
downstream in the same river. If the speed of the river is 4 km/h, find the speed of the
boat in still water.
Answers
Step-by-step explanation:
Let the speed of the boat in still water be= v
When the boat travels upwards, it's going against the current and the current will slow down the boat.
Therefore, its speed will be= (v-5)km/h
Similarly, when it will go downwards, the current will help the boat go faster and its speed will be=(v+5)km/h
Let us assume that the time it took to go 30 km upwards to be T1 and the time it took to go 50 km downwards to be T2.
We know that Time=Distance/Speed
It's been given that T1=T2
Hence, we can say that
30/(v-5) = 50/(v+5)
On solving this equation, v turns out to be 20 km/h which is the required answer.
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 .