Question

III уровень 9. Катер шел 2 ч по течению реки и 3 ч против течения. Всего он прошел 148 км. Найдите собственную скорость катера, если скорость течения реки равна 2 км/ч.

Answer 1

По течение реки   
t=2ч
скорость - х+2 км/ч
Против
t=3ч
скорость х-2 км/ч
Расстояние = 148
Составляем уравнение:
2*(х+2)+3*(х-2)=148
2х+4+6х-6=148
8х-2=148
8х=148+2
8х=150
х=18,75 км/ч - собственная скорость катера
Вроде так

Answer 2

Task Analysis

To solve this problem, we need to find the speed of the boat in still water. We are given the speed of the river's current, the time it took for the boat to travel with the current, and the time it took to travel against the current. We can use this information to calculate the boat's speed in still water.

Given Information

- Time with the current: 2 hours - Time against the current: 3 hours - Total distance traveled: 148 km - Speed of the river's current: 2 km/h

Calculating Boat's Speed in Still Water

Let's denote the boat's speed in still water as b.

When the boat travels with the current, its effective speed is the sum of its speed in still water and the speed of the current: b + 2 km/h.

When the boat travels against the current, its effective speed is the difference between its speed in still water and the speed of the current: b - 2 km/h.

We can use the formula: - Distance = Speed × Time

Using the given information, we can set up the following equations: 1. 2(b + 2) = 148 (for the time with the current) 2. 3(b - 2) = 148 (for the time against the current)

Let's solve these equations to find the boat's speed in still water.

Solution

1. From the first equation: 2(b + 2) = 148 - 2b + 4 = 148 - 2b = 144 - b = 72

So, the boat's speed in still water is 72 km/h.

Therefore, the boat's speed in still water is 72 km/h.