How well can you reason? Math alone will not solve this problem.?

Question

Jet B is following jet A, one mile behind, both traveling at the same speed. Jet A fires a rocket at jet B. Just as the rocket strikes, jet B fires a rocket at jet A. It strikes jet A exactly one mile after it had released the initial rocket. Assume both rockets travel at the same speed relative to the ground. What is the combined distance the rockets traveled ?

It is not necessary to know speed or time. The distance required is the sum of the absolute distance each rocket travels.

Just so you know if you are on the right track, the answer is not 0,1,1.5, or 2.

Answer 1

say R = rocket speed and J = jet speed, then

speed x time = distance
(R+J) time1 = 1 mile [rocket & jetB cover 1 mile distance together]
(R-J) time2 = 1 mile [rocket & jetA opposed]

Total time is 1/(R+J) + 1/(R-J)

JetA x total time = 1 mile [given]

J/(R+J) + J/(R-J) = 1 mile

this leads to quadratic: J^2 + 2JR - R^2 = 0

solve for J: J = R ( sqrt2 -1)

The jet speed is approx .414213 speed of the rocket.

In the time the jet travels 1 mile
The rockets travels 1 / .414213 = 2.414 miles

Answer 2

Since Rocket A is traveling in the opposite direction from Rocket B, the distance Rocket A travels is cancelled out by the opposite distance Rocket B travels to the point where Jet A released Rocket A. Since Jet A traveled a further one mile, that is the extra distance traveled by Rocket B, and the combined distance traveled is thus one mile.

Answer 3

x = speed of jets
y= speed of rockets
y=x-y+x+y=2x

so 1st rocket distance= 2/3 mile
and 2nd rocket distance= 1 1/3 mile
total = 2miles

Answer 4

I need the speed of the jets.

Answer 5

do you want an answer in absolute values or in vector values?

Answer 6

0.
They're equal, but in opposite directions so they cancel out.

Answer 7

I would say 2,414 miles.