Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

Question: Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

Solution:
Let the speed of the second lady be x km/hr
Then, speed of first lady = (x + 2) km/hr

ATQ,
24/x - 24/(x + 2) = 1
⇒ x(x + 2) = 48
⇒ x² + 2x - 48 = 0
⇒ x² + 8x - 6x - 48 = 0
⇒ x(x + 8) - 6(x + 8) = 0
⇒ (x + 8)(x - 6) = 0
⇒ x = 6

Hence, speed of first lady = 8 km/hr
The speed of the second lady = 6 km/hr