Question

Max sneezes every 5 minutes, Lina coughs every 6 minutes, and their dog barks every 3 minutes. If there was sneezing, barking, and coughing at 3:15 PM, when is the next time that these three sounds will happen simultaneously?

Answer 1

Answer: The next time at which the three sounds will happen simultaneously at 3 : 45 PM.

Step-by-step explanation: Given that Max sneezes every 5 minutes, Lina coughs every 6 minutes and their dog barks every 3 minutes.

We are to find the time at which these three sounds will happen simultaneously if there was sneezing, barking, and coughing at 3:15 PM.

We have

the sneezing, barking and coughing happen simultaneously at an interval that is equal to the L.C.M. of 5, 6 and 3 minutes.

Now,

L.C.M. (5, 6, 3) = 30.

Therefore, the sneezing, barking and coughing happen simultaneously at an interval of 30 minutes.

Since there was sneezing, barking, and coughing at 3:15 PM, so the next time at which the three sounds will happen simultaneously is

3 : 15 PM + 30 min = 3 : 45 PM.

Thus, the next time at which the three sounds will happen simultaneously is 3 : 45 PM.

Answer 2

3:45 PM

Explanation:

The least common multiple of 3, 5, and 6 is 30, so the next occurrence will be 30 minutes after 3:15 PM, at 3:45 PM.