A runner hopes to complete a 12,00 m run in less than 30 min. after exactly 25 min, there are still 1000 m to go. The runner must then accelerate at 0.5 m/s^2 for how many seconds in order to achieve the desired time?
the distance run during the final leg is s(t) = v0 t + 1/2 at^2
You don't say what her speed v0 is, but figure it is the average speed achieved so far.
So solve s(t) = 1000