Question

The speed of a boat in still water is9 km/hr. If the boat goes 54 km downstream in 4 hours, find the speed of the stream.
A) 2.5 km/h
B) 4.5 km/h
C) 3.7 km/h
D) 5.7 km/h

Answer 1

Hint:
Here we are going to take speed of stream as x km/hr, when going downstream the speed of the boat in still adds up with the speed of stream, which we will take as \[(9 + x)\] km/hr, as we are given the distance and time taken, so we use the fact that speed is equal to distance upon time, to find the speed of stream.

Complete step by step solution:
Let speed of downstream be x km/hr
Now as given in the question we get
The speed of boat in still stream is 9 km/hr
Also given, the boat goes 54 km in 4 hours.
By which we can say that speed of downstream \[ = 9 + x\] km/hr
So, by which the formula of speed is \[\dfrac{{dis\tan ce}}{{time}} = speed\]
Now on substituting the values we get,
 \[ \Rightarrow \dfrac{{54}}{4} = (9 + x)\]
On multiplying the equation by 4 we get,
 \[ \Rightarrow 54 = 4 \times (9 + x)\]
Now we will multiply 4 with \[(9 + x)\] we will get
 \[ \Rightarrow 54 = 36 + 4x\]
On subtracting 36 from both sides we get,
 \[ \Rightarrow 54 - 36 = 4x\]
On simplification we will get,
 \[ \Rightarrow 18 = 4x\]
On dividing the equation by 4 we get,
  \[ \Rightarrow \dfrac{{18}}{4} = x\]
Hence, we get
 \[ \Rightarrow 4.5 = x\]
Hence the speed of stream is 4.5 km/hr

Therefore, the answer is B.

Note:
Speed is nothing but the amount of distance covered in a certain amount of time.
In water, the direction along the stream is called downstream and the direction against the stream is called upstream.
If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:
Speed downstream \[ = \left( {u\; + v} \right)\] km/hr
Speed upstream \[ = \left( {u\; - \;v} \right)\] km/hr