The proposed bullet train covers a distance of 600 kms in india. The speed of the train will be 200 kmph lesser in its testing phase and thus, the journey time may
increase by 30 min. Find the actual journey time of the train. What is the ratio of x and y
Given : The proposed bullet train covers a distance of 600 kms in india. The speed of the train will be 200 kmph lesser in its testing phase and thus, the journey time may increase by 30 min.
To Find : the actual journey time of the train
Solution:
Distance = 600 km
Actual Journey time = T hrs
Actual Speed = 600/T km/hr
Testing Time = T + 1/2 hrs ( 30 mins = 1/2 hrs)
Testing Speed = 600 / ( T + 1/2)
= 1200/(2T + 1)
1200/(2T + 1) + 200 = 600/T
=> 6/(2T + 1) + 1 = 3/T
=> 6T + (2T + 1) T = 3(2T + 1)
=> 6T + 2T² + T = 6T + 3
=> 2T² + T – 3 = 0
=> 2T² + 3T – 2T – 3 = 0
=> 2T (T – 1) + 3(T – 1) = 0
=> T = 1 , T = – 3/2
Hence actual journey time of the train = 1 hr
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