Question

1. Пасажирський катер пропливає відстань 150 км між двома стоянками по течії річки за 2 год, а проти течії за 3 год. Визначте швидкість катера в стоячій воді та швидкість течії річки. 100 б​

Answer 1

I can answer your question in detail.

1. To find the speed of the boat in still water and the speed of the river current, we need to use the following formulas:

$$v_b = \frac{s}{t}$$

$$v_c = \frac{v_{b1} - v_{b2}}{2}$$

where $v_b$ is the speed of the boat in still water, $s$ is the distance between the stations, $t$ is the time of travel, $v_c$ is the speed of the current, and $v_{b1}$ and $v_{b2}$ are the speeds of the boat with and against the current, respectively.

Using the given data, we can calculate the speeds of the boat with and against the current:

$$v_{b1} = \frac{150}{2} = 75 \text{ km/h}$$

$$v_{b2} = \frac{150}{3} = 50 \text{ km/h}$$

Then, we can find the speed of the current by subtracting the two speeds and dividing by two:

$$v_c = \frac{75 - 50}{2} = 12.5 \text{ km/h}$$

Finally, we can find the speed of the boat in still water by adding or subtracting the speed of the current to either of the speeds with or against the current:

$$v_b = v_{b1} - v_c = 75 - 12.5 = 62.5 \text{ km/h}$$

or

$$v_b = v_{b2} + v_c = 50 + 12.5 = 62.5 \text{ km/h}$$

Therefore, the speed of the boat in still water is 62.5 km/h and the speed of the river current is 12.5 km/h.

This problem is similar to the one solved in [this website](https://urok.in.ua/content/ss-13-tekstovi-zadachi-na-ruh-519-548), where you can find more examples and explanations.