Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction with different velocities, they meet in 8 hours and if they move in opposite directions towards each other they meet in 1 hour 20 minutes. Find the speeds of the cars.

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35 km/h and 20 km/h

35 km/h and 25 km/h

30 km/h and 25 km/h

15 km/h and 20 km/h

answer is A.

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Detailed Solution

It is given that if the two cars move in the same direction, they meet in 8 hours but if they move in the opposite directions, they meet in one hour and 20 minutes.
Distance between A and B is 80 km.
We will form a pair of linear equations and solve them by using elimination method.
Let the speed of the two cars be x km/h and y km/h.
We know that the

s p e e d = d i s t a n c e t i m e

.
Hence,

d i s t a n c e = s p e e d × t i m e

.
Since, the time is given as 8h the distance covered by car A and B are 8x and 8y respectively.
When the two cars move in the same direction, then the difference between the distances travelled by two cars is 80 km.
Hence,