Boat sailed 12km against the flow of the river and 5km for the flow. At the same time, he spent so much time as he would need if he sailed 18km on the lake. What is the eats of the boat, if the flow rate of the river 3km / h.
We need to find our own speed of the boat, we denote it x km / h. Considering that the speed of the river flow is km / h watering the speed by flow and cons:
(x + 3) km / h – for the flow;
(x – 3) km / h – speed against the flow;
x km / h – own speed or speed of movement on the lake.
The distance that the boat sailed is known by the condition for the equation regarding the time of its movement:
12 / (x – 3) + 5 / (x + 3) = 18 / x
12x² + 36x + 5x² – 15x = 18x² – 162
x² – 21x – 162 = 0
D = 1089, x1 = -6; x2 = 27.
The negative value of X is not suitable, so the eigen speed of the boat is 27 km / h.
Answer: 27 km / h.
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