3 fully identical planes (P1, P2 and P3) take off at the same time.

P2 and P3 are used as support planes: they can instantly refuel P1 and each other.

P2 and P3 must both return safely to the starting point: meaning they can't run out of fuel.

Using 1 mile per gallon and 300 gallon tanks, by how many miles can P1's range be increased?

Does P2 and P3 have extra tanks for refueling or do they all only have the one tank?

The 3 planes are identical, so all have a 300 gallon tank.

Also identical in speed, of course.

100 miles?

If they go 125 miles, they all have 175 gallons left, if P2 and P3 give P1 50 gal. each they have 125 gal left to return.

Good try Flo, but you can do better than 100 miles

Logically, in my mind, that's all I've got to give. Hopefully someone else can give P1 more.

Try having P3 refill P1 and P2 (back to 300 gallons)
at same time, then returning to start point...

Bit of an improvement:

All three fly 75 miles, leaving them with 225 gals. P3 gives 75 gals each to P1 and P2, leaving them with 300 galls and himself 75. He heads home.

P1 and P2 fly a further 75 miles, leaving them with 225 gals and 150 miles from home. P2 transfers 75 galls to P1 leaving P1 full-up and himdelf just enough to get back for breakfast.

P1 can now fly a further 300 miles, making 450 in total.

You get the job as P2 Pilot, Rog!
Flo, you need to retry your Pilot Exams

Hmmmmm, to much brain strain there. Simple is my motto, so he only gets another 100 instead of 150.