Distance, rate, and time

Question

A student must leave for the campus in 10 minutes or he will be late for class.  Unfortunately, he is snowed in. He can shovel the driveway in 16 minutes, and his brother claims to be able to do it in 14 minutes. If they shovel together, how long will it take to clear the driveway? Will this give enough time for the student to get to the campus?

Answer 1

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.

Answer 2

It will take 8.5 minutes to clear the driveway together