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Q.

State true or false.

13 km/hr is the speed of the steamer upstream if it goes downstream and covers the distance between two ports in 3 hours, covers the same distance in 5 hours when it goes upstream with the speed of the stream as 3km/hr.

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a

True

b

False

answer is B.

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Detailed Solution

We have to check if 13 km/hr is the speed of the steamer upstream if it goes downstream and covers the distance between two ports in 3 hours, covers the same distance in 5 hours when it goes upstream with the speed of the stream as 3km/hr.
We know that upstream indicates the direction in which the stream is moving, whereas downstream indicates the direction in which the stream is flowing.
Let the streamer's speed be a variable,
Then,

speed = D i s t a n c e time

The steamer’s speed being

x

Downstream speed

= (x + 3)

Upstream speed

= (x − 3)

And, the distance between the two ports for downstream

= 3 (x + 3)

......

(1)

The distance between two ports for upstream

= 5 (x − 3)

......

(2)

Calculating the speed of the steamer upstream
Equating the first and second equations as:

3 (x + 3) = 5 (x − 3)

Now multiplying on both sides we get:

3 x + 9 = 5 x − 15

3 x − 5 x = − 15 − 9

Then,

− 2 x = − 24

x = 12

So, the speed of streamer in still water

= 12

km/hr and thus the given statement is false. Therefore, option 2 is correct.

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