Question

a man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. the speed of the stream is

Answer 1

Answer:

1.5 km/h

Explanation:

M = 4.5 km/h

2 * UP = DS

Let, S = x

    UP = 4.5 -x

    DS = 4.5 + x

So,

(4.5 + x) = 2(4.5 - x)

or, 4.5 + x = 9 - 2x

or, 3x = 4.5

or, x = 1.5

Answer 2

A man  can swim in still water at 4.5 km/h but takes twice as long to swim upstream than downstream.

We have to find the speed of the stream.

What are upstream and downstream ?

upstream : it means, an object is going opposite to the flow of a river.

downstream : it means, an object is going along the flow of a river.

for understanding, if we assume x is speed of object in still water and y is speed of stream then

• speed of object in upstream = (x - y)
• speed of object in downstream = (x +y)

here, the speed of a man in still water , x = 4.5 km/h

let the speed of stream is y km/h.

so speed of the man in upstream = (4.5 - y) km/h

speed of the man in downstream = (4.5 + y) km/h

we know, speed = distance/time

it is clear that, if distance remains constant, speed of a particle will be inversely proportional to time.

i.e., speed ∝ 1/time

A/C to question, he takes twice as long to swim upstream as downstream.

∴  $\frac{s_{upstream}}{s_{downstream}}=\frac{t_{downstream}}{t_{upstream}}$

⇒ $\frac{(4.5-y)}{(4.5+y)}=\frac{1}{2}$

⇒ 2(4.5 - y) = (4.5 + y)

⇒ 9 - 2y = 4.5 + y

⇒ 3y = 4.5

⇒ y = 1.5

Therefore the speed of the stream is 1.5 km/h.