Verified answer

Answer:

The speed of the steamer in still water is 25 km/h.

Step-by-step explanation:

Given:

• A steamer travels 90 km downstream in the same time as it takes to travel 60 km Upstream.
• Speed of the stream is 5 km/h

To Find:
Speed of the steamer in still water.

Calculation:

Let, The speed of the steamer is = y km/h

Speed of the stream = 5 km/h

Speed of steamer in the upstream = Speed of steamer - Speed of stream

Speed of steamer in the downstream = Speed of steamer + Speed of stream

Speed of steamer in the upstream = y - 5 km/h

Speed of steamer in the downstream = y + 5 km/h

We know that,

Speed = Distance / Time

Time = Distance / Speed

Time taken to cover 90 km distance in downstream = 90/(y + 5) hour

Time taken to cover 60 km distance in upstream = 60/(y - 5) hour

90/(y + 5) = 60/(y - 5)

or, 3(y - 5) = 2(y + 5)

or, 3y - 15 = 2y + 10

or, y = 25

Hence, The speed of the steamer in still water is 25 km/h. ( ans. )

Answer:

Let speed of steamer in still water = x km/h

Speed of the steamer downstream = x + 5

Speed of the steamer upstream = x - 5

Speed = Distance / time

So time = Distance / speed

Time taken by steamer to travel 90 km downstream = 90/ (x + 5)

Time taken by steamer to travel 60 km upstream = 60/ (x – 5)

Since time taken by the steamer in both cases is the same ,

90 60

------- = ---------

x + 5 x- 5

Now , we will do cross multiplication

90 (x - 5) = 60 ( x + 5)

90x - 450 = 60x + 300

90x - 60 x = 300 + 450

30 x = 750

x = 750/30

x = 25

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