points A and B are 120 km apart on a highway one car starts from A and another from B at the same time. If they travel in the same direction of the different speeds,they meet in 6hr. if they travel towards each other ,they meet in 1hr. what are the speeds of the two cars ?
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Answer:
Let the speed of car I=xkm/hr
And the speed of car II=ykm/hr
Car I starts from point A and Car II starts from point B.
Let two cars meet at C after 6h.
Distance travelled by car I in 6h=6xkm
Distance travelled by car II in 6h=6ykm
since, they are travelling in same direction, sign should be negative 6x−6y=120
⇒x−y=20…(i)
Now, Let two cars meet after 1 hr 12 min 1hr 12min=1+6012=56hr
since they are travelling in opposite directions, sign should be positive.
56x+56y=120
⇒6x+6y=120×5
⇒x+y=100…(ii)
On adding (i) and (ii) , we get x−y+x+y=20+100
⇒2x=120
⇒x=60
Putting the value of x=60 in Eq. (i), we get 60−y=20
⇒y=40
So, the speed of the two cars are 60km/h and 40km/hr respectively.
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