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(By Examveda Team)

Let the speed of the second lady be x km/hr
Then, speed of first lady = (x + 2) km/hr
$$\eqalign{ & \therefore \frac{{24}}{x} - \frac{{24}}{{\left( {x + 2} \right)}} = 1 \cr & \Rightarrow x\left( {x + 2} \right) = 48 \cr & \Rightarrow {x^2} + 2x - 48 = 0 \cr & \Rightarrow {x^2} + 8x - 6x - 48 = 0 \cr & \Rightarrow x\left( {x + 8} \right) - 6\left( {x + 8} \right) = 0 \cr & \Rightarrow \left( {x + 8} \right)\left( {x - 6} \right) = 0 \cr & \Rightarrow x = 6 \cr} $$
Hence, speed of first lady = 8 km/hr
And speed of second lady = 6 km/hr