Imagine that the amount of snow would fill 112 shovels.
The student can clear the snow in 16 minutes so his shovelling rate is 112/16=7 shovels per minute.
His brother’s rate is 112/14=8 shovels per minute. So together they can work at 7+8=15 shovels a minute.
To clear 112 shovels of snow working at the rate of 15 shovels a minute would take 112/15=between 7 and 8 minutes because 7*15=105 and 8*15=120. So 112 shovels comes in between. The actual time is 112/15=7 min 28 secs (7/15 of a minute is 7/15 of 60=28 seconds), enough time for the student to get to campus.