A car completed a journey of 400 km in $$12\frac{1}{2}$$ hrs. The first $$\frac{3}{4}$$ of the journey was done at 30 km/hr. Calculate the speed for the rest of the journey.

$$\eqalign{ & {\text{Total journey = 400}} \cr & \frac{3}{4}{\text{ Journey = 400}} \times \frac{3}{4} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 300{\text{ km}} \cr} $$
Remaining journey = 100 km
Let the speed of car for the rest of journey = x km/hr
According to the question,
$$\eqalign{ & \frac{{300}}{{30}} + \frac{{100}}{x} = 12\frac{1}{2} \cr & 10 + \frac{{100}}{x} = \frac{{25}}{2} \cr & \frac{{100}}{x} = \frac{{25 - 20}}{2} \cr & x = \frac{{100 \times 2}}{5} \cr & x = 40{\text{ km/hr}} \cr} $$