Photo AI

Here are three lamps - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 3

Question 11

Here are three lamps. Lamp A flashes every 20 seconds. Lamp B flashes every 45 seconds. Lamp C flashes every 120 seconds. The three lamps start flashing at the sam... show full transcript

Worked Solution & Example Answer:Here are three lamps - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 3

Step 1

Find the LCM of 20, 45, and 120

96%

114 rated

Answer

To find how many times the lamps flash simultaneously, first determine the least common multiple (LCM) of the flashing intervals:

Factor each number:
- 20: $2^2 \times 5$
- 45: $3^2 \times 5$
- 120: $2^3 \times 3 \times 5$
Take the highest power of each prime factor:
- For 2: $2^3$ (from 120)
- For 3: $3^2$ (from 45)
- For 5: $5^1$ (from all three)

Thus, the LCM is:

$LCM(20, 45, 120) = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360$

The lamps flash together every 360 seconds.

Step 2

Calculate how many times in one hour

99%

104 rated

Answer

Since there are 3600 seconds in one hour, calculate the number of times the lamps flash together:

$\text{Number of flashes} = \frac{3600 \text{ seconds}}{360 \text{ seconds}} = 10$

Thus, the three lamps will flash together 10 times in one hour.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;