Question

A boat can go 72 km downstream in 4 hours and 36 km upstream in 3 hours. Calculate speed of boat in still water.
A) 15 km/hr
B) 12 km/hr
C) 18 km/hr
D) 24 km/hr

Answer 1

Hint: Speed is defined as the distance covered by any object divided by the time taken to cover that distance.
Where Distance is the total length of the path covered by that object.
\[Speed = \dfrac{{Distance}}{{Time}}\]
Moving water is known as a stream.
If the boat is moving in the opposite direction of the stream, then it is known as upstream. And the net speed of boat is given by the formula given below,
\[ \Rightarrow Speed{\text{ }}of{\text{ }}boat\;\;in{\text{ }}still{\text{ }}water - speed{\text{ }}of{\text{ }}stream\]
If the boat is moving in the same direction as of the stream, then it is known as downstream. And the net speed of boat is given by the formula given below
\[ \Rightarrow Speed{\text{ }}of{\text{ }}boat\;\;in{\text{ }}still{\text{ }}water + speed{\text{ }}of{\text{ }}stream\]
Still water means the water is at rest i.e. stationary and \[speed{\text{ }}of{\text{ }}stream{\text{ }} = 0km/hr\]

Complete step-by-step answer:
 Given,
Distance covered in downstream \[ = 72km\]
Time taken to go through downstream \[ = 4hrs\]
Distance covered in upstream \[ = 36km\]
Time taken to go through downstream \[ = 3hrs\]
Let us assume that speed of boat in still water as x km/hr and speed of stream as y km/hr,
As we know that \[Speed = \dfrac{{Distance}}{{Time}}\]
Case 1. While going upstream
Net speed of boat \[ = (x - y)km/hr\]
i.e. \[ \Rightarrow (x - y) = \dfrac{{72}}{4} = 18\] -----Eqn (i)

Case 2. While going downstream
Net speed of boat \[ = (x + y)km/hr\]
i.e. \[ \Rightarrow (x + y) = \dfrac{{36}}{3} = 12\] -----Eqn (ii)
Now adding Eqn (i) and Eqn (ii) we get,
\[\begin{gathered}
   \Rightarrow x - y + x + y = 30 \\
   \Rightarrow 2x = 30 \\
\end{gathered} \]
Hence, \[x = 15km/hr\]
i.e. speed of boat in still water \[ = 15km/hr\]

Hence option (A) is correct.

Note: Always check the unit of all the given data. For example, if distance is given in km and speed is given in m/s then convert both the quantity into the same unit.
\[1{\text{ }}km{\text{ }} = {\text{ }}1000{\text{ }}m\]
\[1km/hr = \dfrac{5}{{18}}m/s\]
Also remember that in upstream the speed of boat decreases and in downstream speed of boat increases.