Question

A steamer, going downstream in a river, covers the distance between two towns in 20 hours. Coming back upstream, it covers this distance in 25 hours. The speed of water is 4km/h. Find the distance between the two towns.

Answer 1

Hint: In this question, we are given the speed of water and the speed in which the steamer covers the distance between two towns. We have been asked to find out the distance between two towns. Assume the speed of the boat and use it, find out the speed in downstream and upstream. Now using the formula of speed, distance and time, put in all the values that you have. This will give you two equations. Equate them and then you will get the speed of the boat. Put it in one of the equations and it will give you distance.

Formula used: ${\text{Speed = }}\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$

Complete step-by-step answer:
Let us start by assuming the speed of the boat.
Let the speed of the boat be ${\text{x }}km/hr$.
Given: Speed of water = $4km/hr$
Speed of boat in water (downstream) = $(x + 4)km/hr$
Speed of boat in water (upstream) = $(x - 4)km/hr$
We know that, ${\text{Speed = }}\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$.
It can be rearranged as-
$ \Rightarrow {\text{Distance = Speed}} \times {\text{Time}}$
It is also given that the streamer took 20 hours to go downstream and 25 hours to go upstream. We have the speed of streamers downstream and upstream and have to find the distance. Let us put the values in the formula.
Downstream –
$ \Rightarrow $Distance = $(x + 4) \times 20$
 On simplifying,
$ \Rightarrow $Distance = $20x + 80$ …………..…. (1)
Upstream –
$ \Rightarrow $Distance = $(x - 4) \times 25$
On simplifying,
$ \Rightarrow $Distance = $25x - 100$ ……………….…. (2)
Now since the streamer covered equal distance while going upstream and downstream, we will equate equation (1) and (2),
$ \Rightarrow 20x + 80 = 25x - 100$
Solving for x,
$ \Rightarrow 100 + 80 = 25x - 20x$
$ \Rightarrow 180 = 5x$
Shifting to find the value of x,
$ \Rightarrow x = \dfrac{{180}}{5} = 36$
Therefore, the speed of the boat is $36km/hr$. We will put it in equation (1) to find the distance.
$ \Rightarrow $Distance = $20 \times 36 + 80$
Solving,
$ \Rightarrow $ Distance = $800km$

$\therefore $ The distance between two towns is $800km$.

Note: If you find it difficult to remember the speed in downstream and upstream, you can always remember in this way –
Imagine a waterfall. The water always flows downward. If the boat also follows the same direction as of water, its speed will increase due to the pressure of water. Hence, in this case, the speed is added. This is called downstream because the boat is going down with water.
On the other hand, if the boat goes up the waterfall (water will always flow downward), its speed will decrease because the speed of water will oppose the speed of the boat. In this case, the speed will be subtracted. This is called upstream because water is flowing downward and the boat is going upward.