Solve this

[Chemical]

thanks to all

[rubah]

I asked the guy today, and he said it was 2 helper planes obviously we have a long ways yet to go! unless there was some sort of thing about refueling. I should ask him to break it down.

[Manny]

I think my brain just collapsed into itself and became antimatter.

[Tavrobel]

I asked the guy today, and he said it was 2 helper planes obviously we have a long ways yet to go! unless there was some sort of thing about refueling. I should ask him to break it down.

Three planes depart:
(x, t) = 0, 0
P₁ = 1
P₂ = 1
P₃ = 1

(x, t) = 1/8, 1
P₁ = 3/4
P₂ = 3/4
P₃ = 3/4

(x, t) = 1/8, 2
P₁ = 1
P₂ = 1
P₃ = 1/4

(x, t) = 1/4, 3
P₁ = 3/4
P₂ = 3/4
P₃ = 0 (port)

(x, t) = 1/4, 4
P₁ = 1
P₂ = 1/2
P₃ = 1 (port)

(x, t) = 3/4, 5
P₁ = 0
P₂ = 1 (port)
P₃ = 1 (port)

(x, t) = 3/4, 6
P₁ = 0
P₂ = 2/3
P₃ = 2/3
P₂ and P₃ are traveling in the negative direction, traveling 1/6 of the way, consuming 1/3 of the tank.

(x, t) = 3/4, 7
P₁ = 0
P₂ = 1 (x = -1/6)
P₃ = 1/3

P₂ travels from -1/6 to -1/4, which is a distance of 1/12, consuming 1/6th of the tank.

(x, t) = 3/4, 8
P₁ = 0
P₂ = 5/6 (x = -1/4)
P₃ = 0 (port)

Move 1/3 of the tank.

(x, t) = 3/4, 9
P₁ = 1/3
P₂ = 1/2
P₃ = 1 (port)

P₃ must travel out. P₁ and P₂ move another 1/6th forward, consuming 1/3 of the tank. 3/4 + 1/6 = 11/12.

(x, t) = 11/12, 10
P₁ = 0
P₂ = 1/6
P₃ = 5/6 (x = -1/12)

(x, t) = 11/12, 11
P₁ = 1/6
P₂ = 1/6
P₃ = 4/6

(x, t) = 1, 12
P₁ = 0
P₂ = 0
P₃ = 1/2

So basically, all three planes went together at first. Plane 3 gave its fuel to the first two, which caused it to head back, and the other two to travel on. The first two went further, and the second plane gave its fuel to the first plane. Plane 2 heads back, while plane 3 refuels. Plane 1 spends its gas, while plane 2 and 3 are refueled.

Plane 2 and 3 go a distance, until plane 3 gives its fuel to plane 2. Plane 3 heads back, while plane 2 makes its way to the first plane. Plane 2 refuels plane 1 once again, while plane 3 is refueled. Plane 3 heads out to refuel both plane 1 and plane 2 and head to port from the negative x direction. All three planes land down.