Question

A steamer, going downstream in a river, covers the distance between two towns in 16
hours. Coming back upstream, it covers this distance in 24 hours. If the speed of the
water is 4 km/hr, find the speed of the steamer in still water and the distance between
two towns.

Answer 1

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

Answer 2

Answer:

speed of streamer = 20km/hr, distance = 374km

Step-by-step explanation:

Distance = speed x time

let distance be x

speed of streamer = y (let), and that of river = 4

from condition (1)

x = (4+y) x 16

x = 64 + 16y eqn (1)

from condition (2)

x = (y - 4) x 24

x = 24y - 96 eqn (2)

from eqn (1) and eqn(2)

64 + 16y = 24y - 96

8y = 160

y = 160/8

y = 20 km/hr

hence x = (4+y) x 16

x = (4+20) × 16

x = 24× 16

x = 384 km