The distance between two railway stations is 1176 km. To cover this distance, an express train takes 5 hours less than a passenger train while the average speed of the passenger train is 70 km/h less than that of the express train. The time taken by the passenger train to complete the travel is:
Answer & explanation
Correct answer: option 4
We are given that ,
Speed = \(\frac{Distance}{Time}\)
Let us consider that ,
Speed of express train = s km/h
Speed od passenger train = ( s - 70 ) km/h
According to question,
\(\frac{1176}{s-70}\) - \(\frac{1176}{s}\) = 5
\(\frac{1176( s - s + 70) }{s(s-70)}\) = 5
\(\frac{1176 (70) }{s(s-70)}\) = 5
s² - 70s - 16464 = 0
By solving it ,
s = 168 km/h
The speed of express train = 168 - 70
= 98 km/h
Time taken by express train to travel 1176 km
= \(\frac{1176}{98}\)
= 12 hours