The man will be facing West.

Here's the breakdown:

1. Starts facing North.
2. Turns 45 degrees clockwise. This brings him to face North-East (45 degrees to the right of North).
3. Turns 135 degrees anti-clockwise. Since an anti-clockwise turn is the same as turning left, 135 degrees to the left of North-East takes him beyond North and completes a full circle plus an additional 90 degrees to the left. 90 degrees left of North is West.

Therefore, even though the total degrees turned don't cancel each other out (45 + 135 = 180), the net effect due to the opposite directions of the turns is to move him 90 degrees to the left, resulting in him facing West.

Here's how to find the middle number:

1. Total sum of all 15 numbers:

• Average of all numbers = 576
• Number of numbers = 15
• Total sum = Average * Number of numbers = 576 * 15 = 8640

2. Combined sum of first 7 and last 7 numbers:

• Average of first 7 numbers = 573
• Average of last 7 numbers = 579
• We can find the combined sum of the first 7 and last 7 numbers by multiplying their respective averages by the number of elements in each group and adding them: Combined sum = (573 * 7) + (579 * 7) = 4011 + 4053 = 8064

3. Sum of the middle number:

• We already found the total sum of all numbers (8640) and the combined sum of the first 7 and last 7 (8064).
• The middle number won't be included in either of those groups.
• Therefore, to find the middle number, subtract the combined sum from the total sum: Sum of middle number = Total sum - Combined sum = 8640 - 8064 = 576

Since there's only one middle number, its sum represents its actual value.

Therefore, the middle number is 576.

We can find the difference between the smallest and largest number (range) by solving the given information about the ratio and difference.

Here's how:

1. Let the numbers be:

   • First number: 11x (where x is a constant representing the proportion)
   • Second number: 13x
   • Third number: 15x

2. Difference between sum of first and second and thrice the third: We can translate this part of the problem into an equation:

   • 3 * 15x - (11x + 13x) = 441

3. Simplify the equation:

   • 45x - 24x = 441

4. Combine like terms:

   • 21x = 441

5. Solve for x:

   • x = 441 / 21
   • x = 21 (We can choose this value of x as it represents the proportion between the numbers)

6. Find the actual numbers:

   • First number: 11x = 11 * 21 = 231
   • Second number: 13x = 13 * 21 = 273
   • Third number: 15x = 15 * 21 = 315

7. Difference (range): Now, find the difference between the largest and smallest number:

   • Largest number - Smallest number = 315 - 231 = 84

Therefore, the difference between the smallest and largest number is 84.

Alvin's speed was 27 kilometers per hour (kmph).

We can find speed using the formula: speed = distance / time.

Here's how to calculate it:

1. Distance: We are given that the distance covered is 1620 km.

2. Time: The time taken is 60 hours.

3. Speed: Speed = 1620 km / 60 hours

4. Calculate: Speed = 27 kmph

Therefore, Alvin traveled at a speed of 27 kmph.

Ashton and Brooks together can complete the work in 40 days.

We can solve this using the concept of rates. Here's how:

• Rate of Ashton: He can finish the work in 60 days, so his rate is 1/60 per day (1 unit of work done every 60 days).
• Rate of Brooks: He can finish the work in 120 days, so his rate is 1/120 per day.
• Combined Rate: When they work together, their rates add up. So, the combined rate is 1/60 (Ashton's rate) + 1/120 (Brooks's rate) = 1/40 per day.

Time taken together: If their combined rate is 1/40 per day (they complete 1/40 unit of work every day), it will take them 1 / (1/40) days to finish the entire work. This is simply the reciprocal of the combined rate, which is 40 days.

Therefore, Ashton and Brooks together can complete the work in 40 days.