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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 point A=xkm/hr. and car speed from point B=ykm/hr.

Distance = speed × time
Distance from A=x×7=7x
Distance from B=y×7=7y
If they travel in the same direction, they meet in 7 hours. Point A and B are 70km apart.
7x7y=70
xy=10         …(i)

if they travel towards each other they meet in one hour. Point A and B are 70km apart.
x+y=70             …(ii)

Adding (i) and (ii). we get
2x=80
x=40

substituting x=40 in (i). we get
40y=10
y=30
x=40km/hr  and y=30km/hr.

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