Question

a steamer going downstream in a river covers the distance between two towns in 15hrs and in upstream 20 hrs. The speed of water is 3 km/hr. Find the distance between two towns.

Answer 1

let x=speed of steamer in still water
x+3=speed of steamer downstream
x-3=speed of steamer upstream


distance=travel time*speed (same for both directions)
..
15(x+3)=20(x-3)
15x+45=20x-60
5x=105
x=21
distance=15(x+3)=15*24=360
distance between two towns=360 km

Answer 2

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