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Doctor Jones starts an appointment every 20 minutes - OCR - GCSE Maths - Question 18 - 2018 - Paper 1
Question 18
Doctor Jones starts an appointment every 20 minutes. Doctor Warholm starts an appointment every 35 minutes. The first appointment for both doctors starts at 8.30 am... show full transcript
Worked Solution & Example Answer:Doctor Jones starts an appointment every 20 minutes - OCR - GCSE Maths - Question 18 - 2018 - Paper 1
Step 1
Calculate the least common multiple (LCM) of appointment intervals
Answer
Doctor Jones has an appointment every 20 minutes, and Doctor Warholm has an appointment every 35 minutes. To find the LCM of 20 and 35, we can start by finding the prime factorization:
- 20 = 2^2 × 5^1
- 35 = 5^1 × 7^1
The LCM is found by taking the highest power of each prime factor:
Therefore, the LCM of 20 and 35 is 140 minutes.
Step 2
Determine the next simultaneous appointment time
Answer
The first appointment for both doctors starts at 8:30 am. To find the next time they have an appointment at the same time, we add the LCM of 140 minutes to 8:30 am.
Calculating this:
140 minutes = 2 hours and 20 minutes.
Adding this to 8:30 am gives:
8:30 am + 2 hours 20 minutes = 10:50 am.