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A clock chimes every 20 minutes - OCR - GCSE Maths - Question 6 - 2020 - Paper 1
Question 6
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 6 - 2020 - Paper 1
Step 1
Determine the common time interval
Answer
To find out how often the clock chimes and the light flashes together, we need to determine the Least Common Multiple (LCM) of their intervals:
- The clock chimes every 20 minutes.
- The light flashes every 8 minutes.
More formally, we are looking for LCM(20, 8).
First, we can find the prime factors:
- 20 = 2^2 * 5
- 8 = 2^3
Using the highest powers of all prime factors, we have:
This means the two events will occur together every 40 minutes.
Step 2
Calculate the time intervals from 08:01 to 12:30
Answer
Next, we need to determine how many times the clock and light will align from 08:01 to 12:30.
Starting at 08:00, the first occurrence after that time will be 08:40. The next occurrences can be calculated by adding the LCM (40 minutes) to each subsequent time:
- 08:40
- 09:20
- 10:00
- 10:40
- 11:20
- 12:00
- 12:40 (this is outside the range)
Thus, the occurrences before 12:30 are: 08:40, 09:20, 10:00, 10:40, 11:20, and 12:00.
Step 3