Problem #44
This month we have two related problems.

Amber bikes a distance of 8 miles to work each day. She leaves home
between 7:30 AM and 9 AM. If she leaves x minutes before 9 then
the traffic is such that her average speed for the trip to work is 10 
x/10 mph. Find the time, to the nearest second, when Amber should
leave in order to arrive at work at the earliest possible time.

Matthew also bikes to work. He leaves after 9 AM and finds that if he
leaves x minutes after 9, his average speed is 10+x/10
mph. He has calculated that if wants to arrive at work as early as
possible, his optimal departure time is 9:20 AM. How far does Matthew have
to bike to get to work?
Source: Keith Austin