Points $A$ and $B$ are $100 k m$ apart. a car starts from $A$ and another from $B$ at the same time. If they go in the same direction they meet in $5 h r$ and if they go in opposites directions they meet in $1 h r$ , find the product of their speeds.

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Solution

Let the speed of the law which sates from place $A = x$ km/h
the speed of the car which starts from place $B = y$ km/h
Case-I- when the car haves in same direction.
Distance = time x speed
$= 5 x$ km
The distance covered by the car which starts from place $A = 5 x$
The distance covered by the car which starts from place $B = 5 y$
$A C - B C = A B$
$5 X - 5 Y = 100$
$x - y = 20$ .......(1)
Case - ii When the car moves in opposite direction
The distance covered by the car which starts from place $A = 1 x$ km
The distance covered by the car which
starts from place $B = 1 y$ km
$A C + B C = A B$
$x + y = 100$ ........(2)
Adding equation (1) and (2)
$2 x = 120$
$x = 60$
putting $x = 60$ in equation (2)
$60 + y = 100 \Rightarrow y = 40$
The speed of the car which starts from place $A = 60$ km/h
The speed of the car which starts from place $B = 40$ km/h
So, product of their speed is $2400 k m / h$

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