01. A Car travels the first half of a Motorway Journey at an average speed of 40 mph, and the second half of the journey at an average speed of 60 mph. What is the average speed for the entire journey?
02. Out of 100 women surveyed leaving Harrods, 83 had a white bag, 77 had black shoes, 62 carried an umbrella and 95 wore a ring. What is the minimum number of women who must have had all four items?
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Answers:
02. Out of 100 women surveyed leaving Harrods, 83 had a white bag, 77 had black shoes, 62 carried an umbrella and 95 wore a ring. What is the minimum number of women who must have had all four items?
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Answers:
01. "48 mph".
Explanation:
Say the journey takes 120 miles.
The first half of the journey (60 miles) takes 60÷40 = 1.5 hours, the second half takes 60/60 = 1.0 hour. So, the journey of 120 miles takes 1.5 + 1.0 = 2.5 hours and therefore, the average speed is 120÷2.5 = 48 mph.
02. "17".
Explanation:
Add the number of items together, which gives 83 + 77 + 62 + 95 = 317 among 100 women.
This gives three items to each and four items to 17 of these women.
The least number of women to have all three items is, therefore, 17.
Explanation:
Say the journey takes 120 miles.
The first half of the journey (60 miles) takes 60÷40 = 1.5 hours, the second half takes 60/60 = 1.0 hour. So, the journey of 120 miles takes 1.5 + 1.0 = 2.5 hours and therefore, the average speed is 120÷2.5 = 48 mph.
02. "17".
Explanation:
Add the number of items together, which gives 83 + 77 + 62 + 95 = 317 among 100 women.
This gives three items to each and four items to 17 of these women.
The least number of women to have all three items is, therefore, 17.
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