A car starts at A and reaches a destination in 8 hours. If it travels first and second half at the speed of 80 km/hr and 100 km/hr respectively then the distance between A and destination is -

Let,
The distance between A and destination be X
The total time taken by the car to cover X = 8 hours
Since X/2 by 80km/hr and remaining X/2 by 100km/hr
Then by Time = distance/speed, we have
(X/2)/80 + (X/2)/100 = 8
⇒ 1/2 {(X/80 + X/100)} = 8
⇒ X/80 + X/100 = 16
⇒ (5X + 4X)/400 = 16
⇒ 5X + 4X = 6400
⇒ 9X = 6400
⇒ X = 6400/9
⇒ X = 711.11
Hence 711.11 km is the required answer.