Free Response Solution–Math: Problem 1

Since it takes Mary 15 minutes to drive to work at a speed of 45 miles per hour, Mary’s work destination is 45/4 miles from her starting point [because 15 minutes=1/4 hours, distance=(45)(1/4) miles]. If Mary drives at 35 miles per hour on the way home, then it should take her (45/4 miles)/(35 miles per hour)=9/28 hours. In total, Mary’s commute takes (1/4)+(9/28)=4/7 hours.

Note: The first step of this problem uses the identity distance= rate x time, while the second step uses the manipulated form of the identity, time=distance/rate.