# To travel 60 km against the river and 54 km in still water, the steamer needs 4 hours and 30 minutes.

To travel 60 km against the river and 54 km in still water, the steamer needs 4 hours and 30 minutes. To overcome 162 km in stagnant water, the steamer needs 3 hours more time than to overcome 72 km upstream of the same river. Find your own steamer speed and current speed

Let the own speed of the steamer be x km / h, and the speed of the river flow y km / h.

Then the steamer moves against the stream of the river at a speed of (x – y) km / h.

By condition:

60 / (x – y) + 54 / x = 4.5;

162 / x = 3 + 72 / (x – y).

Divide the second equation by 3:

54 / x = 1 + 24 / (x – y).

Let’s substitute in the first:

60 / (x – y) + 1 + 24 / (x – y) = 4.5;

84 / (x – y) = 3.5;

84 = 3.5 * (x – y);

x – y = 24.

Substitute this value into the second equation:

54 / x = 1 + 24/24;

54 / x = 1 + 1;

54 / x = 2;

x = 54: 2;

x = 27 (km / h) – the boat’s own speed.

27 – y = 24;

y = 27 – 24;

y = 3 (km / h) – the speed of the river.

Answer: the boat’s own speed is 27 km / h, the speed of the river is 3 km / h.

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