Question

places A and B are 80 km apart from each other on highway A car starts from A and another from B at the same time if they move in same Direction they meet in 8 hours if they move towards Each Other they meet in 1 hour 20 minutes find the speed of cars

Answer 1

Answer:
Let the speed of car starting from A be 'x' km/h and speed of car starting from B be 'y' km/h.
Total distance=80 km
Also 1 hour 20 mins= 4/3 hour
As per given condition, When car moves in same direction,
Distance travelled by y= 8y km
Distance travelled by x= 8x= 80+8y
Now, Equation formed is 8x=80+8y
=> 8x-8y=80
=> x-y=10 ----(1)
Similarly, For opposite direction,
Distance travelled by x= (4/3)x
Distance travelled by y= (4/3) y
Also total distance covered= 4/3*x+4/3y
=> 80= 4x+4y/3
=> 240= 4x+4y
=> 60=x+y ----(2)
Solving Equation (1) and (2)
60=x+y ----(2)
x-y=10 ----(1)
=> x= 10+y ----(3)
Substituting the value of (3) in (2) we get,
60= 10+y+y
=> 60-10=2y
=> 50=2y
=> 25=y
Also, x=10+y=> x= 10+25=> x=35
Therefore Speed of car starting from A is 35km/h
Speed of car starting from B is 25km/h
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Answer 2

Let the speed of the first car which starts from A = x km /hr

Speed of the second car which starts from B = y km / hr

Time = distance / speed

Distance between two places A andB are 80km d = 80 km

i ) if the cars move in same direction

Relative speed of them = ( x + y )km/hr

Time = 8hr

d = 80km

8 = 80 / ( x + y )

x + y = 80 / 8

x + y = 10 ------( 1 )

ii ) if two cars moving opposite direction, Relative speed = ( x - y ) km / hr

Time = 1 hr 20 minutes

= ( 1 + 20 / 60 ) hr

= ( 80/60)

= 4/3 hr

d = 80km

4/3 = 80 / ( x -y )

x -y = ( 80 × 3 ) / 4

x - y = 60-----( 2 )

Add ( 1 ) and ( 2 ) , we get

2x = 70

x = 35

Put x = 35 in ( 1 ) we get ,

y = 25

so,

Speed of the first car = x = 35km/hr

Speed of the second car = 25km /hr

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