Solving Inequalities: Need Help with Part (a)?

[mopit_011]

Homework Statement

An object, constrained to move along the x axis, travels a dis-
tance d1 with constant velocity v1 for a time t1 . It then instan-
taneously changes its velocity to a constant v2 for a time t2 ,
traveling a distance d2 . (a) Show that (v1d1+v2d2)/(d1+d2) is greater than or equal to (v1t1+v2t2)/(t1+t2).
(b) Under what conditions is this an equality?

Relevant Equations

v = v0 + at
x = x0 + v0t + (at^2/2)

I’m not sure of how begin solving for the inequality. How do I begin solving part (a)? Could I have a hint? Thank you!

 

[haruspex]

A good start would be to write the expression for the difference between them.