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 speed of car starting from A = x km/hr
and the speed of car starting from B = y km/hr
Case I : When they travel in the same direction

Distance travelled by car A = AP = `x xx 5` km (Dist. = speed `xx` time)
Distance travelled by car B = BP = y `xx` 5 km
But, we have AB = 100 km
implies AP - BP = 100
implies 5x - 5y = 100 implies x - y = 20 ...(1)
Case II : When they travel in opposite directions

Distance travelled by car A = AQ = x `xx` 1 km
Distance travelled by car B = BQ = y `xx` 1 km
But, we have AB = 100 km
implies AQ + BQ = 100 implies x + y = 100 ...(2)
Adding equations (1) and (2), we get
2x = 120 implies x = 60 km/hr
Putting x = 60 in equation (2), we get
y = 100 - 60 = 40 km/hr
`therefore` Speed of car A = 60 km/hr and speed of car B = 40 km/hr