Phil strung two sets of lights around the window of his store. The first set of lights blinks every 30s and the second every 45s. How often do the sets of lights blink at the same time?

Every 90 seconds, the two sets of light blink together.

Step-by-step explanation:

Given that there are two sets of lights.

First light blinks at every 30s and

Second light blinks at every 45s

To find:

How often the sets of lights blink together?

Solution:

As per given statement,

First light blinks after 30s, 60s, 90s, 120s, 150s, 180s, ........

Second light blinks after 45s, 90s, 135s, 180s, .....

If we look at the common time, shown by underlining it, the two sets of light blink at the same time after 90s, 180s, ...... and so on.

So, the two lights blink together after every 90s.

This can also be solved by finding LCM (Least Common Multiple) of the two numbers i.e. 30 and 45.

Let us have a look at the factors of 30 and 45.

30 = 2 3 5

45 = 3 3 5

So, LCM = 2 3 3 5 = 90

So, after every 90s, the lights will blink together.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s