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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 and if they move in opposite directions they meet in 1 hr 20 minutes. Find the speed of the both cars.
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
=> 8x8y=80
=> xy=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)
xy=10 (1)
=> x= 10+y (3)
Substituting the value of (3) in (2) we get,
60= 10+y+y
=> 6010=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