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

## 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.

⇒7x−7y=70

⇒x−y=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

40−y=10

∴y=30

∴x=40km/hr and y=30km/hr.