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Question

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

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Solution

## Let the speed of car starting from A=x km/hr and speed of car starting from B=y km/hr.The relative speed of A with respect to B when moving in the same direction =x−y km/hr.The relative speed of A with respect to B when moving in opposite direction =x+y km/hr.Distance between A and B=80 km.We know, Time=DistanceSpeedFrom the above information, we have,80x−y=8and80x+y=1+2060=43or,80x−y=8⇒10=x−y⇒x−y=10....(i)Also,80x+y=43⇒240=4(x+y)⇒x=60−y....(ii)Substituting (ii) in (i), we get,x−y=10⇒60−y−y=10⇒60−2y=10⇒2y=50⇒y=25Substituting y=25 in equation (ii), we get,x=60−y⇒x=60−25⇒x=35Thus, the speed of car starting from A=x=35 km/hr and speed of car starting from B=y=25 km/hr.

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