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Amitabh covered a distance of 96 km two hours
faster than he had planned to. This he achieved by
travelling 1 km more every hour than he intended to
cover every 1 hour 15 minutes. What was the speed
at which Amitabh travelled during the journey?
faster than he had planned to. This he achieved by
travelling 1 km more every hour than he intended to
cover every 1 hour 15 minutes. What was the speed
at which Amitabh travelled during the journey?
Most Upvoted Answer
Amitabh covered a distance of 96 km two hoursfaster than he had planne...
Given:
- Distance covered by Amitabh = 96 km
- Amitabh covered the distance in 2 hours less than planned
- Amitabh traveled 1 km more every hour than he intended to cover every 1 hour 15 minutes
To find:
- The speed at which Amitabh traveled during the journey
Assumptions:
- Amitabh had initially planned to cover the distance in "t" hours
Approach:
1. Let's assume Amitabh initially planned to cover the distance in "t" hours. So, his planned speed would be 96/t km/h.
2. Amitabh traveled 1 km more every hour than he intended to cover every 1 hour 15 minutes. This means he covered 1 km extra in every (1 hour 15 minutes) - (1 hour) = 15 minutes = 1/4 hour.
3. So, his actual speed would be (96 + 1/t) km/h.
4. Amitabh covered the distance in 2 hours less than planned, so his actual time taken would be t - 2 hours.
5. Using the formula: Distance = Speed * Time, we can equate the planned distance and actual distance covered to find the value of "t" and then calculate the actual speed.
Calculation:
Planned distance = Distance covered in planned time = Planned speed * Planned time
96 = (96/t) * t
96 = 96
This equation is always true, which means any value of "t" would satisfy it.
Actual distance = Distance covered in actual time = Actual speed * Actual time
96 = (96 + 1/t) * (t - 2)
96 = 96(t - 2) + 1
96 = 96t - 192 + 1
96t = 287
t = 287/96
t = 2.989
Actual speed = (96 + 1/t) km/h
= (96 + 1/2.989) km/h
= 96.334 km/h
Answer:
The speed at which Amitabh traveled during the journey was 96.334 km/h.
- Distance covered by Amitabh = 96 km
- Amitabh covered the distance in 2 hours less than planned
- Amitabh traveled 1 km more every hour than he intended to cover every 1 hour 15 minutes
To find:
- The speed at which Amitabh traveled during the journey
Assumptions:
- Amitabh had initially planned to cover the distance in "t" hours
Approach:
1. Let's assume Amitabh initially planned to cover the distance in "t" hours. So, his planned speed would be 96/t km/h.
2. Amitabh traveled 1 km more every hour than he intended to cover every 1 hour 15 minutes. This means he covered 1 km extra in every (1 hour 15 minutes) - (1 hour) = 15 minutes = 1/4 hour.
3. So, his actual speed would be (96 + 1/t) km/h.
4. Amitabh covered the distance in 2 hours less than planned, so his actual time taken would be t - 2 hours.
5. Using the formula: Distance = Speed * Time, we can equate the planned distance and actual distance covered to find the value of "t" and then calculate the actual speed.
Calculation:
Planned distance = Distance covered in planned time = Planned speed * Planned time
96 = (96/t) * t
96 = 96
This equation is always true, which means any value of "t" would satisfy it.
Actual distance = Distance covered in actual time = Actual speed * Actual time
96 = (96 + 1/t) * (t - 2)
96 = 96(t - 2) + 1
96 = 96t - 192 + 1
96t = 287
t = 287/96
t = 2.989
Actual speed = (96 + 1/t) km/h
= (96 + 1/2.989) km/h
= 96.334 km/h
Answer:
The speed at which Amitabh traveled during the journey was 96.334 km/h.
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Amitabh covered a distance of 96 km two hoursfaster than he had planned to. This he achieved bytravelling 1 km more every hour than he intended tocover every 1 hour 15 minutes. What was the speedat which Amitabh travelled during the journey?
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