Bunuel wrote:

A lighthouse blinks regularly 5 times a minute. A neighboring lighthouse blinks regularly 4 times a minute. If they blink simultaneously, after how many seconds will they blink together again?

A. 20

B. 24

C. 30

D. 60

E. 300

Assume that they both blink at 0 seconds. It turns out that 0 must be the start time.*

The number of seconds after which they blink together

again?

Lighthouse #1 blinks 5 times

per minute1 minute = 60 seconds

L #1 blinks: \(\frac{60secs}{5}=12\), i.e., every 12 seconds

Lighthouse #2 blinks 4 times a minute

L #2 blinks: \(\frac{60secs}{4}=\) every 15 seconds

LCM of 12 and 15 is 60

AND there are only 60 seconds in one minute

We have to start at 0 in order to satisfy both conditions (that #1 and #2 blink 5 and 4 times per 1 minute AND that they blink again simultaneously).

The LCM = 60 seconds = 1 minute

= start time 0, end time 60

The next time that #1 and #2 blink together again is after 60 seconds.

Answer D

Write it outIn about 30 seconds this problem can be solved with a little brute force.

List the times at which each light blinks. Find the match.

L #1 blinks every 12 seconds at

12, 24, 36, 48,

60(Stop there to check. L #2's rate of every 15 seconds has a units digit of 5;

it will hit only numbers that end with 5 or 0)

L #2 blinks every 15 seconds at 15, 30, 45,

60They blink together again 60 seconds later.

Answer D

**1) #1 and #2 must coincide a second time. Each must blink 5 and 4 times respectively within a minute

2) the LCM of 12 and 15 is 60

3) but there are only 60 seconds in one minute

-- The LCM (when they will strike together again) and

-- the time in seconds in which each must strike a certain number of times

-- are the same.

0 is a multiple of 60.

From second 1 to second 60 of one minute, there is exactly one number at which both lights can blink together again: 60

4) we are stuck.

We must make the first simultaneous blink at 0 in order to "fit in" a multiple of 60 before the clock resets.
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