Two ladies simultaneousely leave cities A and B connected by a strainght road and travel towards each other. The first lady travels 2km/h 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?

Let the speed of first lady be (v + 2)km/h and speed of second lady will be v km/h.
Total distance = 24 km
For first lady, Speed = Distance/Time
v + 2 = 24/t ...(i)
Let time taken by first lady to cover distance of 24 km be t h.
Then, time taken by second lady to cover same distance will be(t + 1)h.
For second lady, Speed =Distance/time
v = 24/(t + 1) ...(ii)
Form Eqs.(i) and (ii), we get
24/t - 2 = 24/(t + 1)
⇒ (24 - 2t)/t = 24/(t + 1)
⇒ (24 - 2t)(t + 1) = 24t
⇒ 24t - 2t² + 24 - 2t = 24t
⇒ 2t² + 2t - 24 = 0
⇒ t² + t - 12 = 0
⇒ t² + 4t - 3t - 12 = 0
⇒ t(t + 4) -3(t + 4) = 0
⇒ (t - 3)(t + 4) = 0
⇒ t = 3, -4
∴ t = 3 (t ≠- 4)
∴ The distance travelled by the first lady in one hour
= 24/t = 24/3 = 8 km
And distance travelled by the second lady in one hour
= 24/t + 1
= 24/3 + 1 = 6 km