Question

Бабушка мама и внучка решили пойти купаться на озеро в одном километре от дома.Чтобы прийти на озеро одновременно,мама вышла из дома,когда бабушка уже прошла 100 метров от дома,а внучка вышла из дома,когда мама была в 100 метров от дома.Какое расстояние было от бабушки до внучки,когда вышла внучка,если все трое шли на озеро с постоянной скоростью?

Answer 1

Если скорость постоянная то 100+100=200 расстояние от внучки до бабушки

Answer 2

Problem Analysis

In this problem, we are given that a grandmother, mother, and granddaughter decide to go swimming in a lake that is one kilometer away from their house. We are also given that they all walk at a constant speed. The mother starts walking when the grandmother is already 100 meters away from the house, and the granddaughter starts walking when the mother is 100 meters away from the house. We need to determine the distance between the grandmother and the granddaughter when the granddaughter starts walking.

Solution

Let's assume that the speed of the grandmother, mother, and granddaughter is the same and equal to v meters per second. We can use the formula distance = speed × time to calculate the time it takes for each person to reach the lake.

Let's denote the time it takes for the grandmother to reach the lake as t1, the time it takes for the mother to reach the lake as t2, and the time it takes for the granddaughter to reach the lake as t3.

We know that the grandmother has already walked 100 meters when the mother starts walking. Therefore, the distance the mother needs to walk is 1 kilometer minus 100 meters, which is 900 meters. Using the formula distance = speed × time, we can write the equation 900 = v × t2.

Similarly, we know that the mother has already walked 100 meters when the granddaughter starts walking. Therefore, the distance the granddaughter needs to walk is 1 kilometer minus 100 meters, which is 900 meters. Using the formula distance = speed × time, we can write the equation 900 = v × t3.

Since the speed is the same for all three people, we can set t1 = t2 = t3 = t.

Now, let's calculate the time it takes for each person to reach the lake.

From the equation 900 = v × t2, we can solve for t2: t2 = 900 / v.

From the equation 900 = v × t3, we can solve for t3: t3 = 900 / v.

Since t1 = t2 = t3 = t, we can conclude that t1 = t2 = t3 = 900 / v.

Now, let's calculate the distance between the grandmother and the granddaughter when the granddaughter starts walking.

When the granddaughter starts walking, the grandmother has already walked 100 meters, and the granddaughter needs to walk 900 meters. Therefore, the distance between the grandmother and the granddaughter is 900 - 100 = 800 meters.

Answer

The distance between the grandmother and the granddaughter when the granddaughter starts walking is 800 meters.

Explanation

When the granddaughter starts walking, the grandmother has already walked 100 meters, and the granddaughter needs to walk 900 meters. Therefore, the distance between the grandmother and the granddaughter is 900 - 100 = 800 meters.

Example

Let's consider an example to illustrate the solution. Suppose the speed of the grandmother, mother, and granddaughter is 2 meters per second. Using the formula distance = speed × time, we can calculate the time it takes for each person to reach the lake:

- The time it takes for the grandmother to reach the lake is t1 = 100 / 2 = 50 seconds. - The time it takes for the mother to reach the lake is t2 = 900 / 2 = 450 seconds. - The time it takes for the granddaughter to reach the lake is t3 = 900 / 2 = 450 seconds.

When the granddaughter starts walking, the grandmother has already walked 100 meters, and the granddaughter needs to walk 900 meters. Therefore, the distance between the grandmother and the granddaughter is 900 - 100 = 800 meters.

Please note that the values used in this example are for illustration purposes only and may not reflect the actual values in the problem.