Let speed of faster car = x Km/ hSpeed ofslowercar = y km /hRelative speed when both cartravelsinsame direction= x - yIf the cars travel in thesame directionat different speeds, they meet in 5 hoursSpeed = distance/ timeTotal distance = 100 kmSpeed x – y = 100/5X – y = 20Add y both side we getX = 20 + y …(1)Relative speed when both cartravelsin opposite direction = x + yIf they travel towards each other, they meet in 1 hour.Speed = distance/ timeTotal distance = 100 kmSpeed x + y = 100/1Plug the value of x form equation first we get20 + y + y = 1002y = 80Y = 40Plug the value of y in equation first we getX = 20 + 40X = 60

Hence speeds are 40 Km /h and 60 Km /h

Consider the two cars starting from the pointsandwhich are 100 km apart to beand, respectively.

Consider the speed of carandto bexkm/hr andykm/hr, respectively.We are to find the speed of the cars.When the two cars move in the same directions, they meet at a point in 5 hours. Let this point be.Therefore,The distance travelled by car X = AQ = 5xkmThe distance travelled by car Y = BQ = 5ykmClearly, AQ - BQ = AB

Therefore, (i)

When the two cars move towards each other, they meet at a point betweenandin 1 hour. Let this point beP.

Therefore,The distance travelled by car X = AP =xkmDistance travelled by Y car Y = BP =ykmClearly,

Therefore, (i)We add the equations (i) and (ii),By substituting the value ofxin equation (ii), we haveTherefore, the speeds of the car X and car Y are 60 km/hr and 40 km/hr.

let the speed=x ,ditance =yfor the sum of direction x-y=100/5=20 eq 1.for opposite directions x+y=100/1=100 eq2 .add 1and 2 x+y=100x-y=202x=80 x=40put in 1 x-y=100y=100-40y=60 km/hr