1. Grade 9 Math
Problem of the Week

2. Problem #1 (Sept 21)
How long will it take a mile-long train going 20 miles per hour to get completely through a 2-mile-long tunnel?

3. Solution Week #1
9 minutes. If the train is going 20 mph, it will travel 1 mile in 3 minutes. It will take the engine 6 minutes to go through the tunnel, but it will take another 3 minutes for the caboose to go 1 mile to clear the tunnel.

4. Problem #2 (Sept 28)
A princess is in love with a dashing knight. Unfortunately, the king prefers another suitor for his daughter. The king has locked her in the castle’s tower. The castle is surrounded by a moat that is 10 yards wide. The knight wants to cross the moat, but he has only two 9.75 yard planks and no way to fasten them together. How can the brave knight bridge the moat?

5. Solution #2
Place one board diagonally across the corner of the moat. Place the second board from the midpoint of the first board to the corner of the castle to form a T.

6. Problem #3 (Oct 5)
How much money would you make in 8 days if you made 8 dollars every time the hands of a clock formed a 90 degree angle?

7. Solution #3
$2816.
Right angles occur twice each hour, except that the second right angle between 2 o’clock and 3 o’clock occurs exactly at 3 o’clock, which is also the first occurrence between 3 o’clock and 4 o’clock. The same thing happens at 9 o’clock. Therefore, only 22 right angles occur in a 12-hour period, or 44 in a 24-hour period. Since 352 right angles occur in 8 days, you will earn $2816.

8. Problem# 4 (October 19)
What is the 99th letter in the pattern ABBCCCDDDD . . .

9. Solution #4
N. The place of the letter in the alphabet is significant. Since C is the third letter of the alphabet, the pattern has three Cs. Since D is the fourth letter, the pattern has 4 Ds. One way to solve this problem is by organizing the information in a table.

10. Problem #5 (October 26)
Elizabeth visits her friend Andrew and then returns home by the same route. She always walks 2km/h when going uphill, 6km/h when going downhill and 3km/h when on level ground. If her total walking time is 6 hours, then what is the total distance she walks in km?

11. Solution #5 x - Distance of Uphill Y - Distance of Downhill
Z - Distance Level Ground
Total walking time=6=(x/2+y/6+z/3)+(x/6+y/2+z/3)(This is used for her walking back --- uphill turns to down hill and downhill turns to uphill)
6(x/2+y/6+z/3+y/2+x/6+z/3)=36 36=4(x+y+z) ===> x+y+z=36/4=9 ====>
She walks 18km in total.

12. Problem #6 (Nov 2) How Many Birthdays?
A man was born on February 29, He died on January 29, How many actual birthdays did he get to celebrate during his life (not counting the day he was born as a birthday)? Hint: Don’t forget about leap years.

13. Solution #6
Solution 18. February 29 occurs every four years is a leap year, so the man celebrated his February 29 birthday in these years: 1932, 1936, 1940, 1944, 1948, 1952, 1956, 1960, 1964, 1968, 1972, 1976, 1980, 1984, 1988, 1992, 1996, and 2000 but not 2004 because he died before his birthday.

14. Problem #7 November 17
If it takes two men two hours to dig a hole 3 meters long, 3 meters wide, and 3 meters deep, how long would it take the same two men to dig a hole 6 meters long, 6 meters wide, and 6 meters deep if they worked at the same rate?

15. Solution #7
16 hours. The first hole has a volume of 3 × 3 × 3 = 27 cubic units. The new hole has a volume of 6 × 6 × 6 = 216 cubic units; 216/27 shows that 8 smaller holes would fit into the larger hole. In other words, the new hole is twice as wide, twice as long, and twice as deep as the original, so it would take 2 × 2 × 2 = 8 times as long. Each of the smaller holes took 2 hours, so it will take 16 hours (2 × 8 = 16) to dig.

16. Problem #8 November 23
Fluffy the cat was born on 24 June On her first birthday, Fluffy's age in cat terms was equivalent to that of a 15-year-old human. When she turned 2, her age in human years was 24. At the end of her third year, her human age was 28, and when she was 4, her human age was 32. She continued to age 4 years with each birthday. What year will Fluffy turn 100 in cat years?

17. Solution #8
On 24 June 2004, Fluffy can blow out 100 candles if she can stay awake long enough.

18. Problem #9 November 30 Number Roundabout
Rebecca thinks of a one digit number. She multiplies it by 3, adds 8, divides by 2 then subtracts 6. To her surprise she gets the same number that she had thought of in the first place. What is the number?

19. Solution #9 4

20. Problem #10 December 7 Lobster Years
A lobster's age in years is approximately his weight multiplied by 4, plus 3 years. Write this rule of thumb as a linear equation and determine the age of a 5-pound lobster. How much will a 15-year-old lobster weigh?