Answer
The asteroid would have had to arrive $~~5.1~hours~~$ later.
Work Step by Step
We can find the angle $\theta$ between $102^{\circ}~E$ and $25^{\circ}~E$:
$\theta = 102^{\circ}-25^{\circ} = 77^{\circ}$
We can find the time it takes the Earth to rotate through this angle:
$t = (\frac{77^{\circ}}{360^{\circ}})~(24~h) = 5.1~h$
The asteroid would have had to arrive $~~5.1~hours~~$ later.
