Fountain A squirts water every 24 minutes. Fountain B squirts water every 42 minutes. They squirt water together at 15:19. Find the next time they squirt water together. (b) A school sends 60 students from Year 8 and 105 students from Year 9 to a museum. The school divides these students into groups using the following rules. - The groups must all be the same size. - All students in any group must be from the same year. - There should be as few groups as possible. Find the size of each group and the total number of groups.

GCSE OCR Maths Prime Factors, HCF and LCM: Fountain A squirts water every 2

Fountain A squirts water every 24 minutes - OCR - GCSE Maths - Question 5 - 2021 - Paper 1

Question 5

Fountain A squirts water every 24 minutes. Fountain B squirts water every 42 minutes. They squirt water together at 15:19. Find the next time they squirt water toge... show full transcript

Worked Solution & Example Answer:Fountain A squirts water every 24 minutes - OCR - GCSE Maths - Question 5 - 2021 - Paper 1

Step 1

Find the next time they squirt water together.

96%

114 rated

Answer

To determine when the two fountains will squirt water together next, we need to find the least common multiple (LCM) of their squirting intervals.

Calculate the LCM of 24 and 42:
- The prime factorization of 24 is: $24 = 2^3 \times 3^1$
- The prime factorization of 42 is: $42 = 2^1 \times 3^1 \times 7^1$
- The LCM is found by taking the highest power of each prime:
  - For 2: $2^3$
  - For 3: $3^1$
  - For 7: $7^1$
Hence, $\text{LCM}(24, 42) = 2^3 \times 3^1 \times 7^1 = 168$
Convert LCM to minutes:
- The next squirting together time will occur 168 minutes after 15:19.
Add 168 minutes to 15:19:
- 168 minutes is equivalent to 2 hours and 48 minutes.
- Adding this to 15:19 gives:
  - 15:19 + 2:48 = 18:07

Thus, the next time they squirt water together is at 18:07.

Step 2

Find the size of each group and the total number of groups.

99%

104 rated

Answer

To find the size of each group and the total number of groups, follow these steps:

Determine the total number of students:
- Total students = 60 (Year 8) + 105 (Year 9) = 165 students.
Find the greatest common divisor (GCD):
- The size of each group must divide both 60 and 105 evenly.
- Calculate the GCD:
  - Prime factorization of 60: $60 = 2^2 \times 3^1 \times 5^1$
  - Prime factorization of 105: $105 = 3^1 \times 5^1 \times 7^1$
- Common factors involve 3 and 5:
  - Thus, GCD = 15.
Determine size of each group and number of groups:
- Size of each group = 15 students.
- Total number of groups = $rac{165}{15} = 11$ groups.

Therefore, each group will consist of 15 students, and there will be a total of 11 groups.

Fountain A squirts water every 24 minutes - OCR - GCSE Maths - Question 5 - 2021 - Paper 1

Worked Solution & Example Answer:Fountain A squirts water every 24 minutes - OCR - GCSE Maths - Question 5 - 2021 - Paper 1

Find the next time they squirt water together.

Find the size of each group and the total number of groups.

Join the GCSE students using SimpleStudy...