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# Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other they meet in one hour. What are their speeds in km/hr?

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One of the most important and conceptual question from linear equations in two variables in which we have to calculate the speed of two cars if they are at a distance of 70 km and if they travel in same distance try meet in 7 hrs and they travel in opposite directions they meet in 1 hr.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 31

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1. ## Let car speed from pointÂ A=xkm/hr. and car speed from pointÂ B=ykm/hr.

Distance = speedÂ Ã—Â time
âˆ´Â Distance fromÂ A=xÃ—7=7x
Distance fromÂ B=yÃ—7=7y
If they travel in the same direction,Â they meet inÂ 7Â hours. PointÂ AÂ andÂ BÂ areÂ 70kmÂ apart.
â‡’7xâˆ’7y=70
â‡’xâˆ’y=10Â Â  Â  Â  Â  …(i)

if they travel towards each other they meet in one hour. PointÂ AÂ andÂ BÂ areÂ 70kmÂ apart.
x+y=70Â Â  Â  Â  Â  Â  Â  …(ii)

AddingÂ (i)Â andÂ (ii). we get
2x=80
âˆ´x=40

substitutingÂ x=40Â inÂ (i). we get
40âˆ’y=10
âˆ´y=30
âˆ´x=40km/hrÂ Â andÂ y=30km/hr.

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