To get to work in the morning, Amanda cycles for 10 miles at the rate of 12 mph. She makes a 10 minutes stop for a cup of coffee, and then rides a bus for 15 minutes. The speed of the bus is 45 mph.

a. At what time will Amanda get to work if she leaves home at 8:30 AM?

b. At what time must Amanda leave home to get to work at 9:30 AM if she does not stop for coffee?

c. At what rate, in mph, would Amanda have to cycle to get to work by 9:45 am if she leaves her house at 8:30 am and she wants to have a coffee break that is 5 minutes longer than usual?

d. At what rate, in mph, would Amanda have to cycle to get to work by 9:45 am if she leaves her house at 8:30 am she wants to have a coffee break that is 10 minutes longer than usual?