Projectile motion question

If a projectile it sent with an initial velocity "u" from a level surface and an angle "α" write an expression showing the time taken for the projectile to reach the ground, "t" and another expression combining this with the x-component of the motion to calculate the range, R.

Not particularly confused by the question, but I seem to be going round in circles trying to get the answer. Put me out of my misery!

part a)

time for the projectile to reach max hight(Vy = 0)

U*sinα*g*t where g is gravity and t is time

so t(half) = U*sinα/g

then sice thats only to the top of its trajectory you multiply by 2

thus: t(full) = 2*U*sinα/g

part b)

R = Ucosα*t(full)

R=U*cosα*[2*U*sinα/g]

R = U^2*sin2α/g

btw: 2sinαcosα = sin2α