The boat sailed 18 km along the river and returned back, spending 48

| April 27, 2021 | education

The boat sailed 18 km along the river and returned back, spending 48 minutes less than the way upstream. Find your own boat speed if the river speed is 3 km / h.

Let x km / h be the boat’s own speed. Then the speed of the boat when moving with the current is (x + 3) km / h, against the current (x – 3) km / h. The distance is both downstream and against 18 km, so the boat sailed downstream for 18 / (x + 3) hours, against the current for 18 / (x – 3) hours.

Knowing that the boat spent 48 minutes (48/60 = 0.8 hours) less while sailing with the flow, we can make the equation:

18 / (x – 3) – 18 / (x + 3) = 0.8

We multiply all parts of the equation by (x + 3) (x – 3):

18 (x + 3) – 18 (x – 3) = 0.8 (x² – 9)

18x + 54 – 18x + 54 = 0.8x² – 7.2

-0.8x² = -7.2 – 108

-0.8x² = -115.2

x² = -115.2 / (-0.8)

x² = 144

x = 12 (km / h) – own speed of the boat.

Answer: 12 km / h.



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