# CAT Practice : Speed Time, Races

Tale of two cities and a meeting point in between.

## Speed Time - Meeting point

Q.6: Two friends A and B leave City P and City Q simultaneously and travel towards Q and P at constant speeds. They meet at a point in between the two cities and then proceed to their respective destinations in 54 minutes and 24 minutes respectively. How long did B take to cover the entire journey between City Q and City P?
1. 60
2. 36
3. 24
4. 48

Choice A. 60

## Detailed Solution

Let us assume Car A travels at a speed of a and Car B travels at a speed of b. Further, let us assume that they meet after t minutes.

Distance traveled by car A before meeting car B = a * t. Likewise distance traveled by car B before meeting car A = b * t.

Distance traveled by car A after meeting car B = a * 54. Distance traveled by car B after meeting car A = 24 * b.

Distance traveled by car A after crossing car B = distance traveled by car B before crossing car A (and vice versa).

=> at = 54b ---------- (1)
and bt = 24a -------- (2)

Multiplying equations 1 and 2
we have ab * t2 = 54 * 24 * ab
=> t2 = 54 * 24
=> t = 36

So, both cars would have traveled 36 minutes prior to crossing each other. Or, B would have taken 36 + 24 = 60 minutes to travel the whole distance. Choice (A).

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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