Question 723897
(a) The time between 6:18 AM and 9:38 PM is 15 hours and 20 minutes.
In minutes, it is {{{15*60+20=900+20=920}}} minutes.
From that time we must deduct the 1 hour and 25 minutes that the motorist was not driving. (That is {{{60+25=85}}} minutes).
The motorist was driving for {{{920-85=835}}} minutes.
The distance covered was {{{241miles+207miles=448miles}}}
The speed was {{{(448moles/835minutes)(60minutes/1hour)=32&32/167mph=about 32.2mph}}} which rounds to 32mph
Answer: 32 miles per hour (you have this answer) 
 
(b) If the motorist had gone 16 miles per hour faster than the speed you recorded in part (a), at what time (to the nearest minute) would he or she arrive? 
The motorist would have been moving at {{{32mph+16mph=48mph}}}
At that speed, the motorist would have driven 448 miles in
{{{448/48}}}hours={{{9&1/3}}} hours = 9 hours and 20 minutes = about 9.33 hours.
That is the driving time. (It is not 9 hours and 33 minutes. I do not know why you are subtracting that time, or where you got the 1445 from).
In minutes, the driving would have taken {{{(448/48)60=560}}} minutes.
Adding the same 85-minute break to the driving time, the trip would have taken
{{{560 minutes+85minutes=645 minutes}}}= 10 hours and 45 minutes = 11 hours minus 15 minutes
That trip time added to the 6:18 AM trip start time, would mean the trip would end at 5:03 PM. (I calculate it as 6:18 AM plus 11 hours minus 15 minutes = 5:03 PM)
Answer: 5:03 PM
 
(c) If the motorist had gone 20 miles per hour faster than the speed you recorded in part (a), at what time (to the nearest minute) would he or she arrive?
{{{32mph+20mph=52mph}}}
The time to drive 448 miles at 52 miles per hour is
{{{(448/52)}}}hours = {{{(48/52)*60}}} minutes = about 517 minutes (rounding to whole minutes).
Adding the same 85-minute break to the driving time, the trip would have taken
{{{517 minutes+85minutes=602 minutes}}}= 10 hours and 2 minutes.
Ten hours and 2 minutes after the 6:18 AM departure would  be 4:20 PM, the time for arrival at Mooseville.
Answer: 4:20 PM