Prerna starts from Place A at 5 am at constant speed of 50km/h. She halts at Place B for half an hour and then drives at 30 km/h. If she reaches Place C at 8:30 am, which is 100 km away from Place A, how far is Place A from Place B?

Given:

Speed of Prerna for A to B = 50 km/h

Speed of Prerna for B to C = 30 km/h

She halts for 30 mins

Concept used:

Distance = Speed × time

Calculation:

Let the distance between A and B be x km

So, distance between B and C = (100 - x) km

According to the question,

\(\frac{x}{50} + \frac{100-x}{30}= 3 \)

⇒ \(\frac{3x + 500 - 5x}{150} = 3 \)

⇒ - 2x + 500 = 450

⇒ 2x = 50

⇒ x = 25

So, distance between A and B = 25 km

∴ The required distance is 25 km.