Question

A streamer, going downstream covers the distance between two towns in 20 hours. While
coming back upstream, it covers this distance in 25 hours. The speed of water is 4 km/hr.
Find the distance between the two towns.
[Hint: Downstream speed = Speed of streamer + Speed of water and Upstream speed =
Speed of streamer – speed of water]

Answer 1

Answer:

let speed of boat is x km/h and distance between two town is y km

net speed of boat in upstream=(x-4)km/h

net speed of boat in downstream

=(x+4) km/h

now,

according to question,

y/(x+4)=20

y=20 (x+4) ----------------(1)

y/(x-4)=25

y=25 (x-4) -------------------(2)

for equation (1) and (2)

20 (x+4)=25 (x-4)

20x+80=25x-100

180=5x

x=36 km/h

put x=36 in equation (1)

y=20 (36+4)=20 x 40

=800 km

Step-by-step explanation:

Answer 2

In the question, given that :

• Speed of water = 4 km/hr
• Time taken for downstream = 20 hrs
• Time taken for upstream = 25 hrs

We are also given :

• Downstream speed = Speed of stream + Speed of water
• Upstream speed = Speed of stream - Speed of water

Let the unknown speed of the stream be :

• Speed of stream = x km/hr

So, now according to the question :

• Downstream speed = (x + 4) km/hr
• Upstream speed = (x - 4) km/hr

We know that, the distance downstream and distance upstream is same. So :

• Speed = Distance/Time
• (x + 4) = D/20 and (x - 4) = D/25
• 20 (x + 4) = D and 25 (x - 4) = D

Equating them both and solving for x :

• 20 (x + 4) = 25 (x - 4)
• 20x + 80 = 25x - 100
• 20x - 25x = - 100 - 80
• - 5x = - 180
• x = - 180/- 5
• x = 36 km/hr

Therefore, the speed of the steam is 36km/hr.

Finding the distance between the two towns :

• Distance = Downstream speed (or) Upstream speed
• D = 20(x + 4) (or) 25(x - 4)
• D = 20 (36 + 4) (or) 25 (36 - 4)
• D = 20 (40) (or) 25 (32)
• D = 800km = 800km
• Both will be same cuz distance downstream = distance upstream

Therefore, the distance between the two towns is 800km.