Hot Chase...

Algebra Level 2

A gangster's car, is travelling on a straight line on a road in the desert with a constant velocity of 30 m / s e c 30 m/sec He is chased by two police cars , Car A and Car B. Car A is 500 m 500 m away from the Gangster's Car and Car B is 750 m 750 m away from the Gangster's Car. The police cars objective is to catch the gangster's car by the Car A which must overtake the gangster's car and Car B which will come at level to the Gangster's Car.

Car's A velocity is at 40 m / s e c 40 m/sec and Car's B velocity at 45 m / s e c . 45 m/sec.

What will be the distance between Car A and Car B when Car B comes at level to the gangster's car? = a a

After how many seconds will it take for Car B to come at level with the Gangster's Car? = b b

Give the answer as a + b a + b .


The answer is 50.

Arpit MIshra by Arpit MIshra , 21, India

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1 solution

Arpit MIshra
Apr 12, 2015

a = 0 m a = 0 m

b = 50 s e c o n d s b= 50 seconds

The Car A must pass the 500 m 500 m distance at the speed of 40 − 30 = 10 m / s e c 40 - 30 = 10 m/sec

which shall take 500 m 10 m / s e c \frac{500m}{10m/sec}

= 50 s e c o n d s 50 seconds

The Car B however also completes the distance of 750 m 750 m at the speed of 45 − 30 = 15 m / s e c 45 -30 = 15 m/sec

which shall take 750 m 15 m / s e c \frac{750m}{15m/sec}

= 50 s e c o n d s 50 seconds

Therefore they both will be at equal distance with the Gangster's Car and the distance will be 0 m 0 m .

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