Question

Рншить задачу: катер прошел 12км против течение реки 5 км по течению при этом он затратил столько времени сколько ему потребоволось бы если бы он шел 18км по озеру. Какова собственая скорость катера, если скорость течение реки равна 3 км ч

Answer 1

х км/ч - собственная скорость катера

х+3 км/ч - скорость катера по течению

х-3 км/ч- скорость катера против течения

 

 12     5      18

---- + ---- = ---

х-3   х+3     х

 

12х(х+3)+5х(х-3)=18(х-3)(х+3)

12х²+36х+5х²-15х-18х²+162=0

-х²+21х+162=0

х²-21х-162=0

По теореме Виета:

х1=27 (км/ч)- собственная скорость катера

х2=-6 - не удовлетвор.условию задачи

Answer 2

Problem Analysis

We are given that a boat traveled 12 km against the current of a river in a certain amount of time. We are also given that if the boat had traveled 18 km on a lake, it would have taken the same amount of time. We need to find the speed of the boat.

Solution

Let's assume the speed of the boat in still water is x km/h, and the speed of the river's current is 3 km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (x - 3) km/h.

We can use the formula distance = speed × time to calculate the time taken by the boat to travel 12 km against the current:

12 = (x - 3) × time Similarly, when the boat is traveling on the lake, its effective speed is the sum of its speed in still water and the speed of the current. So, the boat's speed on the lake is (x + 3) km/h.

We can use the same formula to calculate the time taken by the boat to travel 18 km on the lake:

18 = (x + 3) × time Since the boat took the same amount of time in both cases, we can equate the two time expressions:

(x - 3) × time = (x + 3) × time

Simplifying the equation, we get:

x - 3 = x + 3

Solving for x, we find:

x = 6

Therefore, the speed of the boat in still water is 6 km/h.

Answer

The speed of the boat in still water is 6 km/h.