Question

Красная Шапочка выезжает на велосипеде из своего дома к избушке бабушки, расположенной на расстоянии L от дома Шапочки. В то же самое время Волк начинает движение к бабушке из своего логова, удаленного от избушки также на расстояние L. Красная Шапочка знает о маршруте Волка: она рассчитала, что если будет двигаться со своей начальной скоростью, Волк доберется до избушки на 4 часа раньше. Если же Красная Шапочка будет двигаться с такой скоростью, что каждый километр она будет преодолевать на k секунд быстрее, то в итоге она обгонит волка на 2 часа. Найдите число секунд k, определяющее увеличение скорости Шапочки. Скорость Волка v2=15 км/ч, скорость велосипеда Красной Шапочки равна v1=12 км/ч. Ответ округлите до целых.

Answer 1

Ответ:

..........4..............

Объяснение:

Answer 2

Problem Analysis

In this problem, we are given that Little Red Riding Hood is riding her bicycle from her house to her grandmother's cottage, which is a distance of L away from her house. At the same time, the wolf starts moving towards the grandmother's cottage from his den, which is also a distance of L away from the cottage. Little Red Riding Hood knows the wolf's route and has calculated that if she moves at her initial speed, the wolf will reach the cottage 4 hours earlier than her. However, if she increases her speed by k seconds per kilometer, she will be able to overtake the wolf by 2 hours. We need to find the value of k, which represents the increase in Little Red Riding Hood's speed.

Solution

Let's assume that Little Red Riding Hood's initial speed is v1 km/h and the wolf's speed is v2 km/h. We are given that v1 = 12 km/h and v2 = 15 km/h.

To solve this problem, we can use the formula:

time = distance / speed

Let's calculate the time it takes for Little Red Riding Hood and the wolf to reach the cottage using their respective speeds.

The time taken by Little Red Riding Hood to reach the cottage is:

time1 = L / v1

The time taken by the wolf to reach the cottage is:

time2 = L / v2

According to the problem, if Little Red Riding Hood moves at her initial speed, the wolf will reach the cottage 4 hours earlier than her. Therefore, we can write the equation:

time2 - time1 = 4

Substituting the values of time1 and time2, we get:

(L / v2) - (L / v1) = 4

Now, let's consider the scenario where Little Red Riding Hood increases her speed by k seconds per kilometer. Her new speed will be v1 + k km/h.

The time taken by Little Red Riding Hood to reach the cottage with the increased speed is:

time3 = L / (v1 + k)

According to the problem, if Little Red Riding Hood moves at this increased speed, she will overtake the wolf by 2 hours. Therefore, we can write the equation:

time2 - time3 = 2

Substituting the values of time2 and time3, we get:

(L / v2) - (L / (v1 + k)) = 2

Now, we have two equations:

(L / v2) - (L / v1) = 4 (L / v2) - (L / (v1 + k)) = 2

We can solve these equations to find the value of k.

Solution Steps

1. Substitute the given values into the equations. 2. Solve the equations to find the value of k.

Let's solve the equations to find the value of k.

Solution

Substituting the given values into the equations:

(L / 15) - (L / 12) = 4 (L / 15) - (L / (12 + k)) = 2

Simplifying the equations:

(4L - 5L) / 60 = 4 (2L(12 + k) - 15L) / (15(12 + k)) = 2

Simplifying further:

-L / 60 = 4 2L(12 + k) - 15L = 30(12 + k)

Solving the first equation:

-L / 60 = 4 -L = 240 L = -240

Since L cannot be negative, we discard this solution.

Now, let's solve the second equation:

2L(12 + k) - 15L = 30(12 + k)

Expanding and simplifying:

24L + 2Lk - 15L = 360 + 30k

Combining like terms:

11L + 2Lk = 360 + 30k

Rearranging the equation:

2Lk - 30k = 360 - 11L

Factoring out k:

k(2L - 30) = 360 - 11L

Dividing both sides by (2L - 30):

k = (360 - 11L) / (2L - 30)

Now, let's substitute the value of L into the equation:

k = (360 - 11(-240)) / (2(-240) - 30) k = (360 + 2640) / (-480 - 30) k = 3000 / -510 k = -5.88

Rounding the value of k to the nearest whole number, we get:

k = -6

Therefore, the number of seconds k, which determines the increase in Little Red Riding Hood's speed, is -6.

Answer

The number of seconds k, which determines the increase in Little Red Riding Hood's speed, is -6.