Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively. At 5.00 p. m. all four machines give out a signal simultaneously. At what time will this happen again at the earliest?

6:30 pm

Step-by-step explanation:

Given the following :

Four machines give out a signal at intervals of 24 seconds, 27 seconds, 30 seconds and 50 seconds respectively.

Time when all four machines gave out signal simultaneously = 5:00 pm

To find the time all four will give out the next simultaneous signal :

Take the lowest common factor of the four intervals :

L. C. M of 24, 27, 30, 50

Using the Lowest Common Multiple calculator :

L. C. M. = 5400

5400 seconds.

Adding 5400 seconds to the last time a simultaneous signal was produced :

5:00 pm + 5400 seconds

5400 seconds = (5400/60) = 90 minutes = 1hour 30 minutes

5:00 pm + (1 hour 30 minutes)

= 6:30 pm

13

step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2