# CAT Practice : Speed Time, Races

## Perpendicular Directions

Q.29: Arjun travels from A to B, a distance of 200 Km at the speed of 40 Km/hr. At the same time, Rakesh starts from point C at a speed of 20 Km/hr along a roadwhich is perpendicular to AB. Find the time in which Arjun & Rakesh will be closer to each other?
1. 1.5 h
2. 3.33 h
3. 5 h
4. 4 h

Choice D.4 h

## Detailed Solution

Distance between the two at any time t, D = $sqrt{((200 - 40t)^2 + (20t)^2)}$
One way to calculate is to find the minima using $\frac{dD}{dt}$= 0
=) 1/(2 sqrt(Doesn't matter)) x 2 x (200 - 40t) x -40 + (2 x 20t) x 20) = 0
=) 2 x (200 - 40t) x -40 = -40t x 20
=) 400 - 80t = 20t
=) t = 4 hours.
Alternatively, you can find the right answer by putting the options in the equation.

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