I think 20. the light students are say l/4= 40 so l=160 . the 4 heaviest is l-x+y/4=45 where x is minimum and y is maximum weight. so since l= 160. 160-x+y =180 so y-x = 20

Given data:
- Total number of students = 5
- Average weight of the 4 lightest students = 40 kg
- Average weight of the 4 heaviest students = 45 kg

To find:
- Difference between the maximum and minimum possible average weight overall

Solution:

Step 1: Identifying the minimum and maximum possible weights of the 5th student:
- Let's assume the weights of the 4 lightest students as a, b, c, and d.
- We know that the average weight of the 4 lightest students is 40 kg.
- So, the total weight of the 4 lightest students = 40 kg * 4 = 160 kg.
- Therefore, a + b + c + d = 160 kg.
- Let's assume the weights of the 4 heaviest students as e, f, g, and h.
- We know that the average weight of the 4 heaviest students is 45 kg.
- So, the total weight of the 4 heaviest students = 45 kg * 4 = 180 kg.
- Therefore, e + f + g + h = 180 kg.
- Now, we need to find the minimum and maximum possible weights of the 5th student, i.e., i.
- The minimum possible weight of i can be when a = b = c = d = 40 kg (each student has the average weight).
- In this case, i = 0 kg (to maintain the average weight of 40 kg).
- The maximum possible weight of i can be when e = f = g = h = 45 kg (each student has the average weight).
- In this case, i = 85 kg (to maintain the average weight of 45 kg).

Step 2: Calculating the minimum and maximum possible average weight overall:
- Minimum possible average weight overall = (total weight of all students) / (total number of students)
- Minimum possible total weight = (a + b + c + d + i)
- Therefore, minimum possible average weight overall = (160 kg + 0 kg) / 5 = 32 kg
- Maximum possible average weight overall = (total weight of all students) / (total number of students)
- Maximum possible total weight = (e + f + g + h + i)
- Therefore, maximum possible average weight overall = (180 kg + 85 kg) / 5 = 53 kg

Step 3: Calculating the difference between the maximum and minimum possible average weight overall:
- Difference = Maximum possible average weight overall - Minimum possible average weight overall
- Difference = 53 kg - 32 kg = 21 kg

Answer:
The difference between the maximum and minimum possible average weight overall is 21 kg.