Question 151
Mandy needs to wake up early for attending a mathematics contest. She has set an alarm in her smartphone every 15 minutes since 5:30 am. If an alarm is not pressed off by her or her mother (or anybody else), it will ring for a while, stop for a while, then will ring again 9 minutes later as the first ring, and so on (e.g. if the first alarm is not pressed off, it will ring again at 5:39 am). Also each alarm will work independently. Now suppose each ring-tone lasts for $x$ minutes, and the smartphone has eventually rung for 50 minutes before Mandy wakes up at 6:30 am (assuming no one has pressed off any alarm before that). Find the value of $x$.