Places A and B are 100 km apart on a highway. One car starts from A and another from b at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars

Explanation

Let the speeds of the cars from A and B be x km/hr and y km/hr respectively.
Case I When the two cars move in the same direction :
In this case, them meet at M after 5 hours.

Then, ` AM = 5x ` km
And, BM = 5y km.
` therefore AM - BM = AB rArr 5 x - 5y = 100`
`rArr 5 (x - y ) = 100 rArr x - y = 20" " `...(i)
Case II When the two cars move in the opposite directions :
Let one car move from A to B and let the other move from B to A. Let them meet at N after 1 hour.

Then, AN = x km and BN = y km
` therefore AN + BN = AB rArr x + y = 100" " ` ... (ii)
Adding (i) and (ii), we get ` 60 + y = 100 rArr y= 40 `
Putting x = 60 in (ii), we get `60 + y = 100 rArr y = 40 `
` therefore ` speed of the car from A = 60 km /hr,
and speed of the car from B = 40 km/hr.