# CAT Practice : Speed Time, Races

How quickly must your cousing travel to overtake your uncle - the idea of relative speed.

## Relative Speed

Q.8: Car A trails car B by 50 meters. Car B travels at 45km/hr. Car C travels from the opposite direction at 54km/hr. Car C is at a distance of 220 meters from Car B. If car A decides to overtake Car B before cars B and C cross each other, what is the minimum speed at which car A must travel?
1. 36 km/hr
2. 45 km/hr
3. 67.5 km/hr
4. 18 km/hr

Choice C. 67.5 km/hr

## Detailed Solution

To begin with, let us ignore car A. Car B and car C travel in opposite directions. Their relative speed = Sum of the two speeds = 45 + 54 kmph. = 99kmph. = 99 * ${5 \over 18}$m/s = ${55 \over 2}$m/s = 27.5m/s.
The relative distance = 220m. So, time they will take to cross each other = ${220 \over 27.5}$ = 8 seconds.

Now, car A has to overtake car B within 8 seconds. The relative distance = 50m
=> Relative speed should be at least ${50 \over 8}$m/s = 6.25m/s
=> 6.25 * ${18 \over 5}$kmph = 22.5kmph

Car B travels at 45kmph, so car A should travel at at least 45 + 22.5 = 67.5kmph.

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## More questions from Speed Time, Races

"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi