Question

Продолжительность прогулки грудного ребёнка в первый день составляет 20 мин. Затем она увеличивается ежедневно на 10 мин и доводится до 2 ч в день. На какой по счёту день длительность прогулки достигнет 2 ч и сколько всего времени за эти дни ребёнок проведёт на воздухе?

Answer 1

Решение:

данную задачу решим с помощью арифметической прогрессии:

a₁ = 20 мин - продолжительность в первый день

d = 10 мин - ежедневное увеличение

aₙ = 2 часа = 120 мин - n - день в который продолжительность 2 часа

n - ?

Sₙ - ?, мин общее время на воздухе

Найдем на какой по счёту день длительность прогулки достигнет 2 ч:

aₙ = a₁ + (n - 1)*d

120 = 20 + (n - 1)*10

120 = 20 + 10n - 10

120 = 10 + 10n

10n = 110

n = 110:10

n = 11 - день на который продолжительность прогулки достигнет 2 ч.

Найдем сколько всего времени за эти дни ребёнок проведёт на воздухе S₁₁:

a₁₁ = 120 мин

Sₙ = (a₁ + aₙ)/2*n

S₁₁ = (a₁ + a₁₁)/2*n

S₁₁ = (20 + 120)/2*11

S₁₁ = 140/2*11

S₁₁ = 70*11

S₁₁ = 770 мин проведёт ребёнок на улице;

770 мин = 12 часов 50 мин;

Ответ: на 11 день длительность прогулки достигнет 2 ч, 12 часов 50 мин ребёнок проведёт на воздухе.

Answer 2

Duration of Walks for an Infant

The duration of a walk for an infant on the first day is 20 minutes. Each day, the duration increases by 10 minutes and reaches 2 hours (120 minutes) per day. We need to determine on which day the duration of the walk will reach 2 hours and calculate the total time the child spends outdoors during these days.

To find the answer, we can calculate the number of days it takes for the duration to reach 2 hours and then calculate the total time spent outdoors.

Let's break it down step by step:

1. On the first day, the duration of the walk is 20 minutes. 2. Each day, the duration increases by 10 minutes. 3. We need to find the day when the duration reaches 2 hours (120 minutes).

To calculate the number of days it takes for the duration to reach 2 hours, we can use the following formula:

Number of days = (Total duration - Initial duration) / Increase per day

Let's substitute the values into the formula:

Number of days = (120 minutes - 20 minutes) / 10 minutes

Simplifying the equation:

Number of days = 100 minutes / 10 minutes = 10 days

Therefore, it will take 10 days for the duration of the walk to reach 2 hours.

Now, let's calculate the total time the child spends outdoors during these 10 days:

Total time = Initial duration + (Increase per day * Number of days)

Substituting the values:

Total time = 20 minutes + (10 minutes * 10 days)

Simplifying the equation:

Total time = 20 minutes + 100 minutes = 120 minutes

Therefore, the child will spend a total of 120 minutes (2 hours) outdoors during these 10 days.

To summarize: - The duration of the walk will reach 2 hours on the 10th day. - The child will spend a total of 120 minutes (2 hours) outdoors during these 10 days.

Please note that the information provided above is based on the given scenario and calculations.