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.
