Question

A steamer goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1km/hr, find the speed of the steamer in still water and the distance between the ports.​

Answer 1

Answer:

Given:

Speed of the stream = 1 km/hr

Let the:

Speed of steamer in still water be x km/hr.

We know that:

Downstream = Still water + Stream

$\implies$ $\boxed{\sf{(x+1)\:km/hr}}$

Upstream = Still water – Stream

$\implies$ $\boxed{\sf{(x-1)\:km/hr}}$

And distance:

$\bullet$ Downstream (9 hours) = 9 (x + 1) km

$\bullet$ Upstream (10 hours) = 10 (x – 1) km

Therefore:

9 (x + 1) = 10 (x – 1)

$\implies$ 9x + 9 = 10x – 10

$\implies$ 9x – 10 = – 10 – 9

$\implies$ – x = – 19

$\implies$ x = 19

So:

Speed of steamer in still water is 19 km/hr.

Now:

Distance between the two ports:

$\implies$ 9 (x + 1) km

$\implies$ 9 (19 +1) km

$\implies$ 9 × 20 km

$\implies$ 180 km

Hence:

The speed of the steamer in still water is 19 km/hr and the distance between the ports is 180 km.

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Answered by: Niki Swar, Goa❤️

Answer 2

Answer:

speed of steamer = 19 km/h

distance b/ w the ports = 108 Km