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Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in kmph?
- a)1.25
- b)1.1
- c)11/9
- d)2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Aravind started for the station half a km from his home walking at 1 k...
Distance covered in 3 minutes = 3*(1000/60) = 50
Now he has to cover (500+50)m in (30-3) minutes
Required speed = (550/1000)/(27/60) = 11/9 km/h
Most Upvoted Answer
Aravind started for the station half a km from his home walking at 1 k...
Problem: Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeeded in catching the train. Find his latter speed in kmph?
Solution:
Let the speed at which Aravind returns to his home be x km/h.
Distance from home to station = 0.5 km
Time taken to walk to the station at 1 km/h = distance / speed = 0.5 / 1 = 0.5 hours
After 3 minutes = 3/60 = 1/20 hours, Aravind starts returning home.
Time taken to return home = 1/20 hours
Time taken to travel from home to station = 0.5 / x hours
Total time taken = 0.5 / 1 + 1/20 + 0.5 / x
As Aravind catches the train, the total time taken must be less than or equal to the time of the train's departure.
Let the train's departure time be T.
0.5 / 1 + 1/20 + 0.5 / x ≤ T
Simplifying, we get:
25 + x + 10 / x ≤ 20T
Simplifying further we get,
x² - 10x + 25 ≤ 0
(x - 5)² ≤ 0
Since x² - 10x + 25 is a perfect square, its minimum value is 0.
Therefore, the only possible value of x is 5 km/h.
Hence, Aravind's latter speed is 5 km/h or 11/9 km/h (approx).
Therefore, option C is correct.
Solution:
Let the speed at which Aravind returns to his home be x km/h.
Distance from home to station = 0.5 km
Time taken to walk to the station at 1 km/h = distance / speed = 0.5 / 1 = 0.5 hours
After 3 minutes = 3/60 = 1/20 hours, Aravind starts returning home.
Time taken to return home = 1/20 hours
Time taken to travel from home to station = 0.5 / x hours
Total time taken = 0.5 / 1 + 1/20 + 0.5 / x
As Aravind catches the train, the total time taken must be less than or equal to the time of the train's departure.
Let the train's departure time be T.
0.5 / 1 + 1/20 + 0.5 / x ≤ T
Simplifying, we get:
25 + x + 10 / x ≤ 20T
Simplifying further we get,
x² - 10x + 25 ≤ 0
(x - 5)² ≤ 0
Since x² - 10x + 25 is a perfect square, its minimum value is 0.
Therefore, the only possible value of x is 5 km/h.
Hence, Aravind's latter speed is 5 km/h or 11/9 km/h (approx).
Therefore, option C is correct.
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Community Answer
Aravind started for the station half a km from his home walking at 1 k...
Distance covered in 3 minutes = 3*(1000/60) = 50
Now he has to cover (500+50)m in (30-3) minutes
Required speed = (550/1000)/(27/60) = 11/9 km/h
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Aravind started for the station half a km from his home walking at 1 km/h to catch the train in time. After 3 minutes he realised that he had forgotten a document at home and returned with increased, but constant speed to get it succeded in catching the train. Find his latter speed in kmph?a)1.25b)1.1c)11/9d)2Correct answer is option 'C'. Can you explain this answer?
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