Anita can cover a sure separation in 1 hr 24min by covering two-third of the…

Step-by-Step Solution

To find the aggregate separation (total distance), we use the basic relationship: Time = Distance / Speed.

1. Define Variables:

   • Let the aggregate separation (total distance) be x km.

   • First part of the journey: Distance = (2/3)x, Speed = 4 km/hr.

   • Second part of the journey: Distance = x - (2/3)x = (1/3)x, Speed = 5 km/hr.

2. Convert Total Time to Hours:

   • Total time = 1 hour 24 minutes.

   • 24 minutes = 24/60 hours = 0.4 hours.

   • Total time = 1 + 0.4 = 1.4 hours, which is 14/10 = 7/5 hours.

3. Set up the Equation:

   • Total Time = Time1 + Time2

   • 7/5 = ((2/3)x / 4) + ((1/3)x / 5)

   • 7/5 = x/6 + x/15

4. Solve for x:

   • Find a common denominator for the right side (30):

   • 7/5 = (5x + 2x) / 30

   • 7/5 = 7x / 30

   • Multiply both sides by 30/7:

   • (7/5) * (30/7) = x

   • x = 6.

The aggregate separation is 6 km.