One caution sign flashes ever 4 seconds, and another caution sign flashes every 10 seconds. At a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same time?
A. 6
B. 7
C.14
D. 20
E. 40
LCM(4,10) = 20
noob
To determine when the two caution signs will flash at the same time again, we need to find the least common multiple (LCM) of their flashing intervals.
The flashing interval of the first caution sign is 4 seconds, and the flashing interval of the second caution sign is 10 seconds.
Prime factorize the flashing intervals:
- For the first caution sign: 4 = 2^2
- For the second caution sign: 10 = 2 * 5
To find the LCM, we take the highest power of each prime factor that appears in either factorization:
- The highest power of 2 is 2^2
- The highest power of 5 is 5^1
Therefore, the LCM is 2^2 * 5^1 = 20.
So, the two caution signs will next flash at the same time after 20 seconds.
The correct answer is D. 20 seconds.
To find out how many seconds elapse until the two caution signs flash at the same time again, we need to determine the time it takes for their flashing patterns to align.
First, let's find the time it takes for the first caution sign to flash by itself. Since it flashes every 4 seconds, it will have flashed at the following intervals:
4, 8, 12, 16, 20, 24, ...
Next, let's find the time it takes for the second caution sign to flash by itself. Since it flashes every 10 seconds, it will have flashed at the following intervals:
10, 20, 30, 40, ...
From looking at the patterns, we can see that the first caution sign flashes at a shorter interval than the second caution sign. To determine when they will next flash at the same time, we need to find the least common multiple (LCM) of the flashing intervals of the two signs.
The LCM of 4 and 10 is 20. This means that the two caution signs will next flash at the same time after 20 seconds.
Therefore, the correct answer is option D. 20