The boat has a speed 50 km / h higher than the speed of the motor ship, and therefore it covered

| June 15, 2021 | education

The boat has a speed 50 km / h higher than the speed of the motor ship, and therefore it covered the distance of 210 km in 7 hours 30 minutes faster than the motor ship. Find the speed of the boat.

1. Distance, which the motor ship and the boat sail: S = 210 km;

2. Sailing time of the boat: Tk hours;

3. The motor ship sails this distance in: Tt hours;

4. According to the problem statement: Tk = (Tt – 7.5) hours;

5. The speed of the boat is equal to: Vk km / h;

6. The speed of the ship is equal to: Vt km / h;

7. According to the problem statement: Vk = (Vt + 50) km / h;

6. The equation of motion of the boat in time:

Tt -Tk = 7.5 hours;

S / Vt – S / Vk = S * (1 / Vt – 1 / Vk) =

210 * (1 / (Vk – 50) – 1 / Vk) = 7.5;

10500 = 7.5 * Vk² – 375 * Vk;

Vk² – 50 * Vk – 1400 = 0;

Vk1,2 = 25 + – sqrt (25² – 1400) = 25 + – 45;

A negative root is meaningless;

Vk = 25 + 45 = 70 km / h.

Answer: the speed of the boat is 70 km / h.



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