A steamer going downstream in a river, covers the distance between 2 towns in 15 hours. Coming back upstream, it covers this distance in 20 hours. The speed of the water is 3 km/hr. Find the distance between two towns.
Answers
Answer:
ANSWER
Let the speed of the stream be x km/h.
Given, speed of water =3 km/h
Therefore, downstream speed =(x+3) km/h
and upstream speed =(x−3) km/h
Again, time taken in downstream and upstream is 15 hours and 20 hours respectively.
Now, distance downstream = distance upstream
⇒15(x+3)=20(x−3)
⇒15x+45=20x−60
⇒15x−20x=−60−45
⇒−5x=−105 or x=21 km/h
Therefore, downstream speed =21+3=24 km/h
So, distance between the two towns = Downstream speed × Time taken in downstream
=24×15=360 km
Step-by-step explanation:
Given:
In downstream, streamer cover distance of two towns in 15 hours
In upstream, streamer cover distance of two towns in 20 hours.
Speed of water is 3km/h
To find :
Distance between those two towns?
Solution:
In this given question, we have given that streamer cover distance between two towns in 15 hours during downstream but during upstream, steamer cover distance between two towns in 20 hours.
Notice that in this question, we haven't given speed of streamer. So first of all we need to find speed of streamer.
☯Let suppose that speed of streamer is x
Therefore,
☯Speed of streamer during upstream = (x-3)km/h
☯Speed of steamer during downstream = (x+3)km/h
Now,
we know that streamer cover distance between two towns in 15 hours during downstream but during upstream, steamer cover distance between two towns in 20 hours.
Also distance between those two towns will be same during downstream amd upstream.
Therefore,
Distance covered during downstream = distance covered during upstream
[ We know that distance = speed × time]
\implies⟹ 15(x+3) = 20( x-3)
\implies⟹ 15x + 45 = 20x - 60
\implies⟹ 15x - 20x = -60 - 45
\implies⟹ -5x = -105
\implies⟹ x = \large{\sf{\dfrac{-105}{-5}}}
−5
−105
\implies⟹ x = 21
Therefore,
☯Speed of streamer during upstream = 21 - 3 = 18km/h
☯Speed of streamer during downstream = 21 + 3 = 24km/h
Again,
We have speed of streamer is given and time is also given.
We know that,
Distance = speed × time
We can put any value ( during upstream or during downstream) we will get same values.
\implies⟹ Distance between towns = speed(upstream) × time (upstream)
\implies⟹ distance between towns = 18× 20
\implies⟹ Distance between towns = 360
Therefore,
\large{\boxed{\sf{\pink{Distance\: between\:two\: towns\:is\:360km}}}}
Distancebetweentwotownsis360km