Kim and Om are travelling from points A to B, which are 400 km apart. Travelling at a certain speed Kim takes one hour more than Om to reach point B. If Kim doubles her speed she will take 1 hour 30 mins less than Om to reach point B. At what speed was Kim driving from point A to B ? (In kmph)

Kim and Om are travelling from points A to B, which are 400 km apart. Travelling at a certain speed Kim takes one hour more than Om to reach point B. If Kim doubles her speed she will take 1 hour 30 mins less than Om to reach point B. At what speed was Kim driving from point A to B ? (In kmph) Correct Answer 80 kmph

Let the speed of Kim be a and that of Om be b
Distance between point A and B = 400 km
Then,
$$\frac{{400}}{a} - \frac{{400}}{b} = 1$$
Let,
$$\eqalign{ & \frac{1}{a} = x{\text{ and }}\frac{1}{b} = y \cr & 400x - 400y = 1.....(i) \cr} $$
Speed of km doubles and she will take lets time i.e., 1 hr 30 min than 0 metre
Again,
$$\eqalign{ & \frac{{400}}{b} - \frac{{400}}{{2b}} = \frac{3}{2} \cr & \therefore 400y - 200x = \frac{3}{2} \cr & 800y - 400x = 3 \cr} $$
Solving (i) and (ii), we get
$$\eqalign{ & 400x - 400y = 1 \cr & \frac{{ - 400x + 800y = 3}}{{400y = 4}} \cr & \therefore y = \frac{4}{{100}} = \frac{1}{{100}}{\text{ km}} \cr & \therefore b = 100{\text{ km}} \cr & {\text{Now,}} \cr & \frac{{400}}{a} - \frac{{400}}{{100}} = 4 \cr & {\text{or, }}\frac{{400}}{a} \cr & \therefore a = 80{\text{ kmph}} \cr} $$