Answer:
a) The whole family is together from August 10 to August 12.
(August 10) ≤ t ≤ (August 12)
That is, the whole family is together for almost 3 days.
b) The parents have at least one visitor from August 2 to August 20.
(August 2) ≤ t ≤ (August 20)
That is, for approximately 19 days.
Step-by-step explanation:
English Translation
Angel, Juan and Ricardo are brothers. During the month of August they traveled to visit their parents who live in Huancayo. Angel arrives on August 5 and will stay until before August 12. Juan goes on vacation on August 2, he only has 15 days, so he decides to go from the first day to the last day of his vacation at his parents' house. Ricardo stays at his parents' house from 10 until just before August 20. a) What is the period of time that the whole family will spend together? Make a symbolic representation of your answer. b) What is the period of time that Angel's parents will receive visits? Express it as an interval. Describe and explain with which operation you find your answer.
Solution
- Angel will arrive on August 5 and will stay until before August 12.
Time that Angel spends is given as
August 5 ≤ Angel ≤ August 12
- Juan arrives on August 2 and spends 15 days, meaning, he leaves on August 17
Time that Juan spends is given as
August 2 ≤ Juan ≤ August 17
- Ricardo stays from August 10 to August 20.
Time that Ricardo spends is given as
August 10 ≤ Ricardo ≤ August 20
a) Period that the whole family will spend together
Assuming the parents are ever present at their own house.
Using just the day's number to represent the August days,
5 ≤ Angel ≤ 12
2 ≤ Juan ≤ 17
10 ≤ Ricardo ≤ 20
5 ≤ t ≤ 12
2 ≤ t ≤ 17
10 ≤ t ≤ 20
To obtain the time the whole family is together, we take the maximum of the lower limits and the minium of the upper limits
10 ≤ t ≤ 12
Hence, the whole family is together from August 10 to August 12. That is, the whole family is together for almost 3 days.
b) What is the period of time that Angel's parents will receive visits?
5 ≤ Angel ≤ 12
2 ≤ Juan ≤ 17
10 ≤ Ricardo ≤ 20
5 ≤ t ≤ 12
2 ≤ t ≤ 17
10 ≤ t ≤ 20
To obtain the time the parents will receive visits, we take the minimum of the lower limits and the maximum of the upper limits
2 ≤ t ≤ 20
Hence, the parents have at least one visitor from August 2 to August 20.
That is, for approximately 19 days.
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