On a highway two places A and B are 120 km apart. A car from A and a second car from B start at the same time. If the cars travel in the same direction at different speeds, they meet in 6 hours, however if they travel towards each other, then they meet in 1 hour. What are their speeds?

Solution: Let ‘X’ and ‘Y’ be the two cars starting from places ‘A’ and ‘B’. 

Speed of car ‘X’ = x km/hr,

and Speed of car ‘Y’ = y km/hr

Case 1. When two cars move in the same direction:

Suppose two cars meet at a point P, then

Distance travelled by the car A in 6 hrs is AP = Speed x Time

=> (x km/hr) x (6hr)

=> 6x km ………..(1)

Distance travelled by the car Y in 6 hours is BP = (y km/hr) x (6h)

=> 6y km ………….(2)

Distance between the two places A and B = Distance travelled by the car X – Distance travelled by the car Y

=> AB = AP – BP

using equations (1) and (2), we get

=> 120 = 6x – 6y

=> x-y=20 ………..(3)

Case 2. When two cars move in the opposite directions (towards each other):

Suppose two cars meet at a point Q, then

Distance travelled by the car ‘X’ in 6/5 hours is AQ = (6/5 x km/hr) …….. (4)

Distance travelled by the car ‘Y’ in 6/5 hours is BQ = (6/5 y km/hr) ………(5)

Distance between two places A and B = Distance travelled by the car X + Distance travelled by the car Y

=> AB = AQ + BQ

=> 6/5 x + 6/5 y = 120

=> 6x + 6y = 600

=> x + y = 100 …….(6)

On adding eq.(3) and (6), we get

=> 2x = 120 and x = 60

=> x = 60 and y = 40. Hence, the speed of the two cars are 60 km/hr and 40 km/hr respectively

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