Question 1057601
x are the number of hours from time you leave.
At 52 mph, it takes your friend 32/52 of an hour to drive 52 miles.  
Your speed is 60 mph
You have to make up 32 miles, and you are 8 mph faster than your friend.  It will take you 4 hours, 32/8.
Alternatively, you are gone 60x miles, where x is the number of hours you've driven.  Your friend has gone 52x+32 miles
See them equal
60x=52x+32, units hours
8x=32
x=4 hours
You will have driven 4 hours at 60 mph and gone 240 miles
Your friend will have driven 4 hours at 52 mph and gone 208 miles PLUS the 32 mile head start, for 240 miles.
It will take you 379/60 or 6.31667 hours to get to SF.
.31667*60=19 minutes
You will arrive in SF at 12:19 pm
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At 6 am, your friend has already gone 32 miles and has 347 miles to go.
At 52 mph this will take 6.6730 hours, or 6h40.38m.  Multiply the 0.6730 by 60 to convert decimal hours to minutes.
Your friend will arrive at 12:40.38 pm, and .38 m is .38*60 or 22.8 sec. 12:40.22.8 pm
You can check that by taking 32/52, the fraction of an hour driven before 6 am, which is 0.615 hr or 36.92 m
Your friend needs 7.288 hr  to go to SF (7h17.30m) and left at 6:00-36.92 m or at 5h23.08 m.
Adding the 7h 17.28 min to that is 12:40.38 m