Question

Two places A and B are 120 km apart from each other on highway. One car starts from A and 5
another from B at the same time. If they move in same direction, they meet in 6 hours and if
they move in opposite directions, they meet in 1 hour and 12 minutes. Find the speeds of the
cars.
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Answer 1

$\huge{\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}!$

• 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/hand 40km/hr respectively.

• hope it will help you!!