Given:
Total distance of A to B = 210 km
Same direction, they meet after 1021 hours
Opposite direction,
They meet after 221 hours
Formula used:
Distance = Speed × Time
Time = Distance/Speed
Concept used:
When they are moving in the same direction, the relative speed between the two bodies is the difference of their speeds.
When they are moving in the opposite directions, the relative speed between the two bodies is the sum of their speeds.
Calculation:
Let X and Y be two cars starting from points A and B respectively.
Let the speed of car X be x km/hr and that of car Y be y km/hr.
Case I:
When two cars move in the same directions,
Suppose two cars meet at point Q. Then,
Distance travelled by car X = AQ,
Distance travelled by car Y = BQ
Two cars meet in 1021 hours.
Distance travelled by car X in 21/2 hours =21x/2 km.
⇒ AQ = 21x/2
Distance travelled by car Y in 21/2 hours =21y/2 km.
⇒ BQ = 21y/2
According to the question,
AQ − BQ = AB
⇒ 21x/2 - 21y/2 = 210
⇒ 21/2 × (x - y) = 210
⇒ x - y = 20 ----(i)
Case II
When two cars move in each other(opposite) directions:
Suppose two cars meet at point P. Then,
Distance travelled by car X = AP
Distance travelled by car Y = BP
Two cars meet in 221 hours,
Distance travelled by car X in 221 hours = 5x/2 km
⇒ AP = 5x/2 km
Distance travelled by car Y in 221 hours = 5y/2 km
⇒ BP = 5y/2 km
According to the question,
AP + BP = AB
⇒ 5x/2 + 5y/2 = 210
⇒ 5/2 × (x + y) = 210
⇒ x + y = 84 ----(ii)
Adding equations (i) and (ii), we get
⇒ x - y + x + y = 20 + 84
⇒ 2x = 104
⇒ x = 104/2 = 52 km/h
Putting the value of x in (i), we get,
⇒ x - y = 20
⇒ 52 - y = 20
⇒ y = 32 km/hr
Difference between their speeds = (52 - 32) km/hr = 20 km/hr
∴ The difference between their speeds (in km / h) is 20 km/hr.