# Points A and B are separated by a distance of 100 km. Two cars start moving from these points in a same direction, they meet after 5 hrs. If the cars travel towards each other they meet after 1 hr. What are their speeds?

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speed of car B=y km/hr

CASE 1

two cars travel in the same direction.

relative speed v=x-y km/hr

distance d=100 km, they meet after 5 hrs. therefore t=5 hrs

t×s=distance

5×(x-y)=100⇒ x-y=20.............(1)

CASE 2

two cars travel in the opposite direction

relative speed v=x+y km/hr, d=100 km, they met after 1 hr therefore t=1 hr

t×s=distance⇒1×(x+y)=100⇒x+y=100...............(2)

solving (1) and (2) we get

x=60km/hr y=40 km/hr