Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 3 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 36 km apart. How many kilometres does each lady travel in one hour?

Solution

Let the speed of the second lady = x kmph ∴ Speed of first lady = [if gte msEquation 12]>x [if !msEquation]-->[endif]-->x+ 3 kmph ∴ As per the question `36/x - 36/(x +3) = 1` [if gte msEquation 12]> 36 x [if !msEquation]-->[endif]--> ⇒(36x+108-36x)/(x²+3x) = 1 ⇒108=x²+3x ⇒ x² + 3x - 108 = 0 ∴ [if gte msEquation 12]>x [if !msEquation]-->[endif]-->x² + 12x [if gte msEquation 12]> x [if !msEquation]-->[endif]--> - 9x [if gte msEquation 12]> x [if !msEquation]-->[endif]--> - 108 = 0 ∴ x(x+12) -9(x-12) = 0 (x+12)(x-9) = 0 ∴ x = -12 or 9 kmph Speed cannot be negative, Hence x = 9kmph So speed of two ladies are = x+3 , x = 12kmph & 9kmph