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A person going from Pondicherry to Ootacamond travels 120 km by steamer, 450 km by rail and 60 km by horse transit. The journey occupies 13 hours 30 minutes, and the speed of the train is three times that of the horse-transit and 1(1/2) times that of the steamer. Find the speed of the train.
- a)20 kmph
- b)60 kmph
- c)10 kmph
- d)50 kmph
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A person going from Pondicherry to Ootacamond travels 120 km by steame...
If speed of horse is X, then speed of steamer = 2X and
Speed of train = 3X => (120/2x)+ (450/3x)+(60/x) = 13.5
=> X = 20 km/hr => 3X = 60 km/hr.
Most Upvoted Answer
A person going from Pondicherry to Ootacamond travels 120 km by steame...
Given data:
Total distance travelled = 120 km + 450 km + 60 km = 630 km
Total time taken = 13 hours 30 minutes = 13.5 hours
Let the speed of the steamer be x kmph.
Then, the speed of the horse transit = x/1.5 = 2x/3 kmph (as given, the speed of the train is 1.5 times that of the steamer)
And, the speed of the train = 2x kmph (as given, the speed of the train is three times that of the horse-transit)
Calculation:
Let's assume the time taken by the steamer, train, and horse transit are t1, t2, and t3 respectively.
Then, we have:
t1 + t2 + t3 = 13.5 hours - - - (1) (Total time taken)
t1 = 120/x - - - (2) (Time taken by steamer = Distance/Speed)
t2 = 450/2x - - - (3) (Time taken by train = Distance/Speed)
t3 = 60/(2x/3) = 90/x - - - (4) (Time taken by horse transit = Distance/Speed)
Substituting the values of t1, t2, and t3 in equation (1), we get:
120/x + 450/2x + 90/x = 13.5
Simplifying this equation, we get:
x = 60 kmph
Therefore, the speed of the train is 2x = 120 kmph.
Hence, the correct option is (b) 60 kmph.
Total distance travelled = 120 km + 450 km + 60 km = 630 km
Total time taken = 13 hours 30 minutes = 13.5 hours
Let the speed of the steamer be x kmph.
Then, the speed of the horse transit = x/1.5 = 2x/3 kmph (as given, the speed of the train is 1.5 times that of the steamer)
And, the speed of the train = 2x kmph (as given, the speed of the train is three times that of the horse-transit)
Calculation:
Let's assume the time taken by the steamer, train, and horse transit are t1, t2, and t3 respectively.
Then, we have:
t1 + t2 + t3 = 13.5 hours - - - (1) (Total time taken)
t1 = 120/x - - - (2) (Time taken by steamer = Distance/Speed)
t2 = 450/2x - - - (3) (Time taken by train = Distance/Speed)
t3 = 60/(2x/3) = 90/x - - - (4) (Time taken by horse transit = Distance/Speed)
Substituting the values of t1, t2, and t3 in equation (1), we get:
120/x + 450/2x + 90/x = 13.5
Simplifying this equation, we get:
x = 60 kmph
Therefore, the speed of the train is 2x = 120 kmph.
Hence, the correct option is (b) 60 kmph.
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A person going from Pondicherry to Ootacamond travels 120 km by steamer, 450 km by rail and 60 km by horse transit. The journey occupies 13 hours 30 minutes, and the speed of the train is three times that of the horse-transit and1(1/2)times that of the steamer. Find the speed of the train.a)20 kmphb)60 kmphc)10 kmphd)50 kmphCorrect answer is option 'B'. Can you explain this answer?
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