Reds v Blues

Five of blue’s cannons are surrounding Red base (T). They are all equally spaced apart, and are 300m from T, however, only cannon B is operational. Cannon B is facing T. Cannon B can turn at angular speed 40 degrees per second, and it takes 0.5 seconds for it to shoot. Cannon C is a Blue Base.

A red missile is moving towards C through point X at 340.29 metres per second. At point X, the red missile is equidistant to cannons A and B. Cannons A and B are 58 degrees right and left, respectively, of X’s direction.

Red base Y is equidistant to cannons A and D. Cannons A and D are 58 degrees left and right, respectively, of the direction YT.

Cannon B must shoot at Red base Y to win the war. Missile X must reach Blue base C to win the war. If Cannon B starts turning at the same time as the red missile passes over point X, one side will win.

By how many seconds will this side win?

Give your answer to three decimal places.

Tip: Don’t round your answer until the end!