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Ad libitum [116K]
3 years ago
11

Blue Island is a tourist attraction that can only be reached by ferry. Tourists may visit the island on any day but they must re

turn to the mainland on the same day. Ferries leave the mainland every 40 minutes. The first ferry leaves at 09:00 and the last ferry leaves at 15:00. Ferries leave Blue Island to return to the mainland at 11:00, 12:00, 13:00 and then every 30 minutes until 17:00. The ferry journey in either direction takes 15 minutes. Kenny catches the first ferry from the mainland to Blue Island after 12:00 and wants to spend at least three hours on the island.
a) What is the earliest time that he can expect to arrive back on the mainland?

Each ferry can carry at most 30 tourists.

b) Explain why not every ferry on any given day can carry a full load of tourists.

Last Monday each ferry carried at least 5 tourists
c) (i) What was the greatest possible number of tourists on Blue Island at 11:30?
c) (ii) What was the possible number of tourists on Blue Island at 11:30?
Mathematics
1 answer:
DENIUS [597]3 years ago
6 0

Answer:

i think letter b. explain why not every fairy on a given day can carry whole load of tourist

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Of 100 students,65 are members of a mathematics club and 40 are members of a physics club. if 10 are members of neither club the
alexandr1967 [171]

a. 15 students are members of both clubs

b. 50 students only are members of the mathematics club

c. 25 students only are members of the physics club

Step-by-step explanation:

The given is:

  • There are 100 students
  • 65 are members of a mathematics club
  • 40 are members of a physics club
  • 10 are members of neither club

We need to find how many students are members of

a. both clubs?

b. only mathematics club

c. only physics club

∵ The total number of students = 100

∵ 10 are members of neither club

- Subtract 10 from 100 to find the members of the mathematics

  club or the physics club

∵ 100 - 10 = 90

∴ There are 90 members of the mathematics club or physics club

∴ n(mathematics or physics) = 90

∵ 65 students are members of a mathematics club

∵ n(mathematics) = 65

∵ 40 students are members of a physics club

∴ n(physics) = 40

∵ n(mathematics or physics) = n(mathematics) + n(physics) - n(both)

∴ 90 = 65 + 40 - n(both)

∴ 90 = 105 - n(both)

- Add n(both) to each side

∴ n(both) + 90 = 105

- Subtract 90 from each side

∴ n(both) = 15

∴ 15 students are members of both clubs

a. 15 students are members of both clubs

∵ 65 students are members of the mathematics club

∵ 15 of them are members of the physics club

∴ n(mathematics only) = 65 - 15 = 50

∴ 50 students only are members of the mathematics club

b. 50 students only are members of the mathematics club

∵ 40 students are members of the physics club

∵ 15 of them are members of the mathematics club

∴ n(physics only) = 40 - 15 = 25

∴ 25 students only are members of the physics club

c. 25 students only are members of the physics club

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