A driver traveled from Haifa to Eilat. He covered a third of the distance at a speed of 75 kph (kilometers per hour), a fifth of the remaining distance in one hour, and the rest of the distance at a speed of 80 kph. The distance between Haifa and Eilat is 450 kilometers. If the driver had driven the entire distance at a constant speed, at what speed would he have needed to drive so that the journey from Haifa to Eilat would take exactly the same amount of time?
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Since the total distance is 450 km,
Hence 1/3rd of the distance, i.e, 150 km is covered with 75 kph speed,
Hence time taken = distance/ speed
= 150/75
= 2 hrs
The second part of the journey i.e 1/5th of the rest = 300/5 = 60km is covered in 1 hr.
The rest of the journey i.e. 240 km is covered with 80 kph speed,
so time taken = 240/80
= 3 hrs.
Hence total time taken = 2+1+3 = 6 hrs
Hence constant speed to cover the whole journey , i.e. 450 km in 6 hrs
= speed = distance / time
= 450/6
= 75 kph
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