Sorry took a while for me to dig out my 1978 C 152 Operating handbook.
Under section 5 (performance)
Total trip distance Naples-Opa Locka-Vero Beach-Naples is 303 NM.
Fuel requirements:
Start-up & taxi 0.8 gallons
Climb to 5000' 1.4 gallons assuming standard temp +20 C
Cruise @ 5000' 5gallons/hr @ 99kts.
After climb fuel remaining = 21.76
3.06 hrs @ 99kts - 15.3
_____________________________
Fuel remaining 6.45 gallons
Three approaches @ 15 min per approach, an additional 45 min fuel.
Since you are lower, less leaning different pwr settings and a missed approach fuel burn will be hard to predict but it's at least 5 gallons/hr
45 min approaches 3.75 gallons.
6.45-3.75 = 2.7 gallons left.
This means after planning a 3 hrs 45 min flight assuming a no-wind condition and three approaches fuel left is 2.7 which equals 0.54 hrs= 32 min.
That's not even IFR reserves.
Very tight planning from the start.
Very scary you assume book -figure fuel burn on a 25 year old plane.
Now take into account the vectors at Vero Beach for 15 min, that leaves you
17 min of fuel. Unknown vectoring at Miami, < 17 min of fuel.
Still a request at Fort Myers for a ILS while the gauges must have been near zero already.
This flight should never have been made without a fuel stop enroute.
Would be interesting to know why they decided otherwise anyway.
Plenty of airports by the way enroute from Vero Beach back to Naples.
According to Airnav.com at
http://www.airnav.com/airport/KVRB cheapest fuel at Vero Beach is self service @$3.30/ gallon.
Part of that will be reimbursed by the flight school I'm sure.