Answer
The trip to Vega will take about 26.26 years as measured by clocks on earth.
Work Step by Step
The relative velocity was given to be 0.990c and the trip was 26.00 light years. Therefore;
$time = distance / speed$
$time= 26.00 light years / (.9900c)$
$time= 26.00 * 299 792 458 m / s/ (.9900*299 792 458 m / s)$
$time=26.26 years$
