The motor boat passed the river for 36 km and returned back, spending 5

| April 26, 2021 | education

The motor boat passed the river for 36 km and returned back, spending 5 hours for the entire journey. Current speed = 3 km / h. Find the speed of the boat in still water.

Let’s denote the boat speed by V.

Then the speed of the spoon downstream is (V + 3), and upstream (V – 3) km / h.

The time that the boat will pass downstream is: 36 / (V + 3),

and upstream: 36 / (V – 3).

By condition, the total time is 5 hours.

(36 / (V + 3)) + (36 / (V – 3)) = 5.

((36 x (V – 3)) + (36 x (V +3))) / (V ^ 2 – 3 ^ 2) = 5.

72 x V = 5 x ((V ^ 2 – 3 ^ 2).

5 x V ^ 2 – 72 x X – 45 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 x a x c = (-72) ^ 2 – 4 x 5 x (-45) = 5184 + 900 = 6084.

V1 = -0.6. (Doesn’t fit)

V2 = 15.

Answer: The speed of the boat in still water is 15 km / h.



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