Question

Моторная лодка прошла от одной пристани до другой, расстояние между которыми по реке равно 16 км, сделала стоянку на 40 мин и вернулась обратно через 11/3 ч после начала поездки. Найдите скорость течения реки, если известно, что скорость моторной лодки в стоячей воде равна 12 км/ч.

Answer 1

Скорость течения реки =х км/час. Скорость лодки по течению = 12+х  км/ч, а против течения - (12-х) км/ч. S=V*t  ,тогда t=S/V Время ,которое лодка плыла по течению = 16/(12+х) час Время ...........................................против течения = 16/(12-х) Стоянка 40 мин=2/3 часа 16/(12+х) +16/(12-х) + 2/3 = 3  2/3 16/(12+х)+16/(12-х)=3 16(12-х)+16(12+х)=3(12+х)(12-х) 192-16х+192+16х=3(144-х²) 384=432-3х²  3х²=48  х²=16 , х=±4 Выбираем по смыслу задачи положительное значение х=4

Answer 2

Х скорость течения
12-х скорость против течения
12+х скорость по течению
16/(12+х)+16/(12-х)=11/3-2/3=9/3=3
192-16х+192+16х=432-3х²
3х²=48
х²=16
х=4км/час скорость ткчения

Answer 3

Calculation of River Current Speed

To find the speed of the river current, we can use the formula:

Speed of the boat in still water = Speed of the boat relative to the ground + Speed of the river current

Let's denote the speed of the boat in still water as B and the speed of the river current as C.

Given information: - Distance between the two docks = 16 km - Boat made a stop for 40 minutes - Boat returned back after 11/3 hours (which is equivalent to 3 hours and 40 minutes) from the start of the trip - Speed of the boat in still water = 12 km/h

To solve this problem, we need to set up two equations based on the given information.

Equation 1: Distance = Speed × Time - For the first part of the trip (from one dock to the other), the boat traveled a distance of 16 km. - For the second part of the trip (from the second dock back to the first), the boat also traveled a distance of 16 km.

Equation 2: Time = Distance / Speed - The boat made a stop for 40 minutes, which is equal to 40/60 = 2/3 hours. - The boat returned back after 3 hours and 40 minutes, which is equal to 3 + 40/60 = 11/3 hours.

Let's solve these equations to find the speed of the river current.

Solution:

Using Equation 1, we can set up the following equation for the first part of the trip:

16 = (B + C) × T1 And for the second part of the trip:

16 = (B - C) × T2 Using Equation 2, we can set up the following equation for the stoppage time:

2/3 = 16 / (B + C) And for the return trip:

11/3 = 16 / (B - C) To solve these equations, we can eliminate the variables T1 and T2 by cross-multiplying Equation 1 and Equation 2:

16 × (B + C) = 16 × (B - C)

Simplifying, we get:

B + C = B - C

The C terms cancel out, leaving us with:

2C = 0

Since the coefficient of C is zero, this means that the speed of the river current (C) is zero. Therefore, there is no current in the river.

Answer:

The speed of the river current is 0 km/h.

Please let me know if there's anything else I can help you with!