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A clock chimes every 20 minutes - OCR - GCSE Maths - Question 19 - 2020 - Paper 1
Question 19
A clock chimes every 20 minutes. A light flashes every 8 minutes. The clock chimes and the light flashes together at 08:00. How many times between 08:01 and 12:30 w... show full transcript
Worked Solution & Example Answer:A clock chimes every 20 minutes - OCR - GCSE Maths - Question 19 - 2020 - Paper 1
Step 1
Finding the Least Common Multiple (LCM)
Answer
To determine how many times the clock chimes and the light flashes together, we first find the least common multiple (LCM) of the two intervals: 20 minutes (for the clock) and 8 minutes (for the light).
The LCM can be calculated as follows:
- The prime factorization of 20 is: .
- The prime factorization of 8 is: .
The LCM takes the highest power of each prime factor:
Thus, the clock chimes and the light flashes together every 40 minutes.
Step 2
Calculating the Time Interval
Answer
Next, we need to determine how many 40-minute intervals there are between 08:01 and 12:30.
- Starting from 08:00 (which is when both occur together), the next time they will occur together is at:
- 08:00 + 40 minutes = 08:40
- 08:40 + 40 minutes = 09:20
- 09:20 + 40 minutes = 10:00
- 10:00 + 40 minutes = 10:40
- 10:40 + 40 minutes = 11:20
- 11:20 + 40 minutes = 12:00
- 12:00 + 40 minutes = 12:40
However, the last calculated time (12:40) occurs after 12:30. Therefore, we only count up to 12:00.
Step 3