Question

Допоможіть! 30 балів! Моторний човен курсує вздовж течії річки між двома пунктами, відстань між якими 30 км. Швидкість руху човна відносно води 20 км/год, а течії – 5 км/год. Якою буде швидкість човна відносно куска дерева, що пливе за течією? За який час човен допливе від одного пункту до іншого, рухаючись за течією? Яка середня швидкість руху човна відносно берега за час подорожі від одного пункту до іншого і назад?

Answer 1

Відповідь: Див. додаток

Пояснення:

Answer 2

Motor Boat's Speed and Time of Travel

To calculate the speed of the boat relative to the piece of wood floating downstream and the time it takes to travel between the two points, we can use the following formulas:

1. Speed of the boat relative to the piece of wood: - The speed of the boat relative to the water is 20 km/h, and the speed of the river's current is 5 km/h. Therefore, the speed of the boat relative to the piece of wood floating downstream is the difference between the boat's speed and the river's current, which is 20 km/h - 5 km/h = 15 km/h.

2. Time taken to travel between the two points: - The distance between the two points is 30 km, and the speed of the boat relative to the water is 20 km/h. To find the time taken to travel downstream, we can use the formula: time = distance / speed. Therefore, the time taken for the boat to travel downstream is 30 km / (20 km/h + 5 km/h) = 30 km / 25 km/h = 1.2 hours.

Average Speed of the Boat Relative to the Shore

To find the average speed of the boat relative to the shore for the round trip from one point to the other and back, we can use the following formula:

1. Average speed of the boat relative to the shore: - The average speed for the round trip is the total distance traveled divided by the total time taken. Since the boat travels downstream at 20 km/h and upstream at 15 km/h (20 km/h - 5 km/h), the average speed relative to the shore is the harmonic mean of these two speeds, which is 2 * (20 km/h * 15 km/h) / (20 km/h + 15 km/h) = 2 * (300 km^2/h) / 35 km/h = 17.14 km/h.

Therefore, the speed of the boat relative to the piece of wood floating downstream is 15 km/h, the time taken to travel downstream is 1.2 hours, and the average speed of the boat relative to the shore for the round trip is 17.14 km/h.