A passenger train departs from delhi at 6 p.m. for mumbai.at 9 p.m., an express train,whose average speed exceeds that of the passenger train by 15 kmph leaves mumbai for delhi. two trains meet each other mid-route. at what time do they meet,given that the distance between the cities is 1080 km ?
Answers
Given:
A passenger train departs from delhi at 6 p.m. for mumbai.at 9 p.m., an express train,whose average speed exceeds that of the passenger train by 15 kmph leaves mumbai for delhi. two trains meet each other mid-route.
To find:
at what time do they meet,given that the distance between the cities is 1080 km ?
Solution:
From given, we have,
A passenger train departs from Delhi at 6 p.m. for Mumbai.at 9 p.m., an express train, whose average speed exceeds that of the passenger train by 15 km/hr leaves Mumbai for Delhi.
Let the speed of the passenger train be = x km/hr
Speed of the express train = (x + 15) km/hr
(540/x) - (540/x + 15) = 3 [ 6 pm - 9 pm]
solving the above equation, we obtain a quadratic equation given by,
x² + 15x - 2700 = 0
(x + 60) (x - 45) = 0
x = 45 km/hr
Time taken to meet is = 540/x = 540/45 = 12 hrs.
Therefore, both the trains will meet at 6 pm + 12 hrs = 6 am