Solution:
Given:
Distance between H and O = D km
Average speed = S km/hr
The average speed that gets a person from H to O in a stipulated time is S units. He takes 20 minutes more time than usual if he travels at 60 km/h, and reaches 44 minutes early if he travels at 75 km/h.
Formula:
Speed = Distance/time
Average speed = Total distance/Total time
Calculation:
Let right time for the train to cover its journey (in minutes) be t hrs, then
As we know,
Distance = Speed × Time
According to the question
60 × (t + 20/60) = 75 × (t - 44/60)
⇒ 4 (t + 1/3) = 5 (t - 11/15)
⇒ 4t + 4/3 = 5t - 11/3
⇒ 5t – 4t = 11/3 + 4/3
⇒ t = 11/3 + 4/3
⇒ t = 5 hrs
Distance (D) = 60 × (5 + 20/60)
⇒ D = 60 × (5 + 1/3)
⇒ D = 60 × (16/3)
⇒ D = 320 km
Distance between H and O is 320 km.
Average speed (S) = 320/5 = 64 km/hr
∴ Sum of numerical values of D and S = 320 + 64 = 384
