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. The speed of second lady?

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. The speed of second lady?

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

Now
(24/x) - 24/(x + 2) = 1
{24(x + 2) - 24x} / {x(x + 2)} = 1
(24x + 48 - 24x) / {x(x + 2)} = 1
48/(x² + 2x) = 1
x² + 2x = 48
x² + 2x - 48 = 0
x² + 8x - 6x - 48 = 0
x(x + 8) - 6(x + 8) = 0
(x + 8)(x - 6) = 0
x = 6

Speed of second lady = 6 km/hr.