Mr.kanja,Miss Kanene and Mrs Nyaga have to mark a form three contest for 160 students.They take 5mins,4mins and 12 mins respectively to mark a script.If they all start to mark at 9:00am non-stop,what is the shortest time they can take to complete the marking.i got 60 mins bt the ans says 300.Someone help.
You divide the 300 by 60 to get 5hrs
(t / 5) + (t / 4) + (t / 12) = 160
multiplying by 60 (the LCD) ... 12 t + 15 t + 5 t = 9600
32 t = 9600 ... t = ?
To find the shortest time it would take for all three to complete the marking, we need to find the least common multiple (LCM) of their marking times.
The marking times are as follows:
Mr. Kanja: 5 minutes
Miss Kanene: 4 minutes
Mrs. Nyaga: 12 minutes
The LCM of 4, 5, and 12 is 60. Therefore, they will all meet again after 60 minutes. However, this only represents the first round of marking. After 60 minutes, Mr. Kanja will have marked 12 papers, Miss Kanene will have marked 15 papers, and Mrs. Nyaga will have marked 5 papers.
To find the shortest time they can all complete marking together, we need to find the next multiple of 60 after 60 minutes that is divisible by the number of students (160).
To do this, we can divide 160 by the LCM of 4, 5, and 12 (60).
160 ÷ 60 = 2 remainder 40
This means that after the first cycle of 60 minutes, they still have 40 papers left to mark. They will need another cycle of 60 minutes to complete these.
To find the total time needed:
60 minutes (first cycle) + 60 minutes (second cycle) = 120 minutes
Hence, the shortest time they can take to complete the marking is actually 120 minutes, not 300 minutes.
To determine the shortest time it takes for Mr. Kanja, Miss Kanene, and Mrs. Nyaga to complete marking the scripts, we need to find the least common multiple (LCM) of their marking times.
The LCM is the lowest multiple that is evenly divisible by all the given numbers - in this case, 5, 4, and 12.
To find the LCM, we can follow these steps:
1. Find the prime factors of each number:
- 5: Prime factors are 5.
- 4: Prime factors are 2 * 2.
- 12: Prime factors are 2 * 2 * 3.
2. Express each number as the product of their prime factors:
- 5 is already prime factorized as 5.
- 4 is expressed as 2 * 2.
- 12 is expressed as 2 * 2 * 3.
3. Determine the highest power of each prime factor:
- 2 occurs twice (two 2's) in the prime factorization.
- 3 occurs once in the prime factorization.
- 5 occurs once in the prime factorization.
4. Multiply the highest powers of each prime factor:
- 2^2 * 3^1 * 5^1 = 4 * 3 * 5 = 60.
Therefore, the least common multiple (LCM) is 60 minutes. This means that Mr. Kanja, Miss Kanene, and Mrs. Nyaga will all complete marking the scripts together after 60 minutes.
It seems that there might have been an error in the answer given (300 minutes). The correct answer is indeed 60 minutes.