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:

12 hours

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