Amrita goes to her office from her house at a speed of 32 km/hr and returns at a speed of 34 km/hr. If she takes 66 hours for going and coming back, then find the distance between her office and house. (In km)

Given:

Speed from house to office = 32 km/hr.

Speed from office to house = 34 km/hr.

Total time for the round trip = 66 hours.

Formula Used:

Distance = Speed × Time

Calculation:

Let the distance between Amrita's house and office be d km.

Time taken to travel from house to office = d / 32

Time taken to travel from office to house = d / 34

Total time for the round trip = (d / 32) + (d / 34)

According to the problem, total time is 66 hours.

Therefore,

⇒ (d / 32) + (d / 34) = 66

⇒ d(1/32 + 1/34) = 66

⇒ d(34 + 32) / (32 × 34) = 66

⇒ d(66 / 1088) = 66

⇒ d = 66 × 1088 / 66

⇒ d = 1088

The distance between Amrita's office and house is 1088 km.