The motor boat sailed 54 km along the river and returned back, spending 7 hours 30 minutes

| June 22, 2021 | education

The motor boat sailed 54 km along the river and returned back, spending 7 hours 30 minutes for the entire journey. The speed of the river is 3 km / h. find the speed of the boat in still water.

Let the speed in still water be a.

Then, the time spent on the way downstream in it will be possible to represent through 54 / (a + 3), while the time spent on the return trip can be expressed in the form 54 / (a – 3).

Since we know that it took only 7.5 hours for the road, then it is possible to write down the equation and find out the required speed:

54 / (a + 3) + 54 / (a – 3) = 7.5;

54 (a – 3) + 54 (a – 3) = 7.5 (a2 – 9);

a ^ 2 – 14.4a – 9 = 0;

D = 207.36 + 36 = 243.36 = 15.62;

a1 = (14.4 + 15.6): 2 = 15;

a2 = (14.4 – 15.6): 2 = – 0.6 (not suitable).

Answer: 15 km / h.



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