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Wednesday, August 25, 2010

Non routine(probem and how to solve it)

iii) Gather information and select three non-routine problem and solve using two ore more types of problem solving. Select one strategy that is deemed to be most efficient and justify selection.

Question 1 :

In a non-leap year, which day is exactly in the middle of the year and what time is it?

i) TABLE

a) Understand the problem

§ What is given : Non-leap year

§ What is needed : The day is exactly in the middle and time of the

year.

b) Plan a strategy

§ Construct a problem-solving table

c) Devising

Month

Days

Hour

January

31

744

February

28

672

March

31

744

April

30

720

May

31

744

June

30

720

July

31

744

August

31

744

September

30

720

October

31

744

November

30

720

December

31

744

Total

365 days

1 year = 365 days

6 Month = 365 ÷ 2

= 182.5

§ Assume that 182.5 = 183

§ Total the days start from January until 183 days:-

31 + 28 + 31 + 30 + 31 + 30

= 181 days (June)

§ 181 days (June) + 2 days in July = 183 days. The day that exactly in the middle of the year is = 2nd July.

§ 1 days = 24 hours

§ 24 hours × 365 days = 8760 hours

§ 6 month =8760 ÷ 2

=4380 hours (Until 30th June)

· Total the hours start from January until 4380 hours:-

744 + 672 + 744 + 720 + 744 + 720 = 4344 hours

4380 hours – 4344 hours = 36hours

36 hours = 1 ½ day (in July)

36 hours -24 hours = 12 hours

24 hours = 1 July

12 hours = 2 July ( 12.00 p.m)

ii) DIRECT REASONING

a) Understand the problem

What is given : Non-leap year.

What is needed : The day is exactly in the middle of the year and the time.

b) Plan a strategy

· Use direct reasoning

c) Devising

· Non-leap year = 365 days

· So the middle of the year = 365/2

= 18.5

= 183 days

· January = 31 day

· February = 28 day

· March = 31 day

· April = 30 day

· May = 31 day

· June = 30 day

Total = 181 day

· To get 183 days, so we need to sum 181 days with 2 day in July. Now, day is exactly in the middle of the year is 2nd July.

· Now 1 day = 24 hour

· We need to times 24 hour with the y of every month

· January 31 × 24 = 744 hour

· February 28 × 24 = 672 hour

· March 31 × 24 = 744 hour

· April 30 × 24 = 720 hour

· May 31 × 24 = 744 hour

· June 30 × 24 = 720 hour

· So, we needed to sum January until June 744 + 672 + 744 + 720 + 744 + 720 = 4322 hour

· Here we get 4344 hour until 30 June. After this we need times 1 ½ with 24 hour

· 1 ½ × 24 = 36 hour

· 1 ½ day = 24 ½ hour

· The answer is 2nd July, 12.00 p.m

Q

1 comments:

CMA said...

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