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)
A. 90 kmph
B. 70 kmph
C. 160 kmph
D. 80 kmph
Answer: Option D
Solution(By Examveda Team)
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
$$\eqalign{ & 400x - 400y = 1 \cr & \frac{{ - 400x + 800y = 3}}{{400y = 4}} \cr & \therefore y = \frac{4}{{100}} = \frac{1}{{100}}{\text{ km}} \cr & \therefore b = 100{\text{ km}} \cr & {\text{Now,}} \cr & \frac{{400}}{a} - \frac{{400}}{{100}} = 4 \cr & {\text{or, }}\frac{{400}}{a} \cr & \therefore a = 80{\text{ kmph}} \cr} $$
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
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