A man has to cover a distance of 753 km in 12 hours. If he covers two-thirds of the distance in 2/3 of the time, then what should his speed (in km/hr) be to cover the remaining distance in the remaining time left ?

Given:

Total distance = 753 km

Total time = 12 hours

Distance covered in the first part = \(\frac{2}{3}\) of total distance

Time taken for the first part = \(\frac{2}{3}\) of total time

Formula used:

Distance = Speed × Time

Speed = \(\frac{Distance}{Time}\)

Calculations:

Distance covered in the first part = \(\frac{2}{3} \times 753\)

⇒ Distance covered = 502 km

Remaining distance = Total distance - Distance covered in the first part

⇒ Remaining distance = 753 - 502

⇒ Remaining distance = 251 km

Time taken for the first part = \(\frac{2}{3} \times 12\)

⇒ Time taken = 2 × 4

⇒ Time taken = 8 hours

Remaining time = Total time - Time taken for the first part

⇒ Remaining time = 12 - 8

⇒ Remaining time = 4 hours

Speed required to cover the remaining distance in the remaining time = \(\frac{Remaining\ distance}{Remaining\ time}\)

⇒ Speed = \(\frac{251}{4}\)

⇒ Speed = 62.75 km/hr

∴ The speed should be 62.75 km/hr to cover the remaining distance in the remaining time.