Question

Катер прошел по течению реки 8 км против течения 16 км, затратив на весь путь одну целую одну третью часа.Какова скорость катера по течению если собственная скорость катера равна 20 км/ч

Answer 1

Пусть скорость теч. реки = км/ч
Тогда составим уравнение 8/(20+х)+16/(20-х)=4/3
(160-8х+32+16х-160-4х^2)/(3(40-х^2))=0
(-4х^2+8х+32)/(3(400-х^2))=0   =>  х не равен +20 и -20
-4х^2+8х+32=0  /4
-х^2+2х+8=0
Д=4+4*8=36
х=(-2-6)/(-2)=4 => скорость теч.=4км/ч. Тогда Скорость по теч.=20+4=24км/ч

Answer 2

Problem Analysis

We are given the following information: - The boat traveled 8 km against the current. - The boat traveled 16 km with the current. - The total time taken for the entire journey was 1 and 1/3 hours. - The boat's own speed is 20 km/h.

We need to find the speed of the boat in still water.

Solution

Let's assume the speed of the current is c km/h.

The boat's speed against the current would be 20 - c km/h, and the boat's speed with the current would be 20 + c km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

The time taken to travel 8 km against the current would be 8 / (20 - c) hours.

The time taken to travel 16 km with the current would be 16 / (20 + c) hours.

According to the problem, the total time taken for the entire journey is 1 and 1/3 hours, which is equal to 4/3 hours.

We can set up the following equation based on the given information:

8 / (20 - c) + 16 / (20 + c) = 4/3

To solve this equation, we can multiply both sides by 3 to get rid of the fraction:

24 / (20 - c) + 48 / (20 + c) = 4

Next, we can multiply both sides by (20 - c)(20 + c) to eliminate the denominators:

24(20 + c) + 48(20 - c) = 4(20 - c)(20 + c)

Expanding and simplifying the equation:

480 + 24c + 960 - 48c = 4(400 - c^2)

1440 - 24c = 1600 - 4c^2

4c^2 - 24c + 160 = 0

We can solve this quadratic equation to find the value of c.

Using the quadratic formula: c = (-b ± √(b^2 - 4ac)) / (2a), where a = 4, b = -24, and c = 160.

Calculating the discriminant: b^2 - 4ac = (-24)^2 - 4(4)(160) = 576 - 2560 = -1984

Since the discriminant is negative, the quadratic equation has no real solutions. This means there is no valid value for the speed of the current that satisfies the given conditions.

Therefore, we cannot determine the speed of the boat in still water based on the given information.

Conclusion

Based on the given information, we cannot determine the speed of the boat in still water. The quadratic equation derived from the problem has no real solutions, indicating that there is no valid value for the speed of the current that satisfies the given conditions.