A boat covered the distance of 450km in 13/2 hrs. if the boat covers thefirst two third of the distance at the speed of 75km/hrs then at what speed would itcovers the remaining distance.

13/2 = 6 1/2 hours???

speed at remaining distance ---- x km/h

(2/3)(450)/75 + (1/3)(450)/x = 13/2
300/75 + 150/x = 13/2
times 2x
8x + 300 = 13x

carry on

To find the speed at which the remaining distance is covered, we first need to determine the distance covered in the first two-thirds of the journey.

Given:
Total distance = 450 km
Time taken = 13/2 hrs

To calculate the distance covered in the first two-thirds of the journey:
First two-thirds of the distance = (2/3) * 450 km = 300 km

We know that the boat covers this distance at a speed of 75 km/hr. Therefore, the time taken to cover the first two-thirds of the distance can be determined as:
Time = Distance / Speed
Time = 300 km / 75 km/hr = 4 hrs

Now, we can calculate the remaining distance:
Remaining distance = Total distance - Distance covered in first two-thirds of the journey
Remaining distance = 450 km - 300 km = 150 km

Since the total time taken for the entire journey is 13/2 hrs and we have already accounted for 4 hrs spent on the first two-thirds of the journey, we can calculate the time taken to cover the remaining distance:
Time taken to cover remaining distance = Total time - Time taken for first two-thirds
Time taken to cover remaining distance = (13/2) - 4 hrs = 13/2 - 8/2 = 5/2 hrs

Finally, to find the speed at which the remaining distance is covered, divide the remaining distance by the time taken to cover it:
Speed = Distance / Time
Speed = 150 km / (5/2) hrs = 150 km * 2/5 hrs = 300/5 = 60 km/hr

Therefore, the boat would cover the remaining distance at a speed of 60 km/hr.