Question

A passenger train depart from delhi at 6:00 p.M. For mumbai at 9:00 p.M. In express train whose average speed extrude that of the passenger train by 15 km overuse mumbai from delhi to train meet each other fruit at what time do they meet given that the distance between the cities is 1080km.?

Answer 1

Correct Question :- A passenger train departs from Delhi at 6:00 PM for Mumbai. At 9 PM, an express train, whose average speed exceeds that of the passenger train by 15 km/hour 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 ?

Solution :-

For Passenger Train which Leaves Delhi at 6PM , Let us Assume that :-

• Speed of Passenger Train = x km/h .
• Time taken by Passenger Train to reach Mid - route = y Hours.

Now, we have given that, Express Train, which Leaves Mumbai at 9PM :-

• Speed of Express Train = 15 + Speed of Passenger Train = (x + 15) km/h .
• Time taken by Express Train to reach Mid - route = 3 Hours Less than Time taken by Passenger Train { 9PM - 6PM} = (y - 3) Hours.

As, Both trains meet each other at mid-route , and distance between the cities is 1080km :-

• Conclude that, Both Cover Half the distance = (1080/2) = 540 km = same Distance .

Therefore,

→ Distance covered by Passenger Train = Distance covered by Express Train .

→ (Speed of Passenger Train * Time taken by Passenger Train to reach Mid - route ) = (Speed of Express Train * Time taken by Express Train to reach Mid - route ).

→ x * y = (x + 15)(y - 3)

→ xy = xy - 3x + 15y - 45

→ 15y - 3x = 45

→ 3(5y - x) = 45

→ (5y - x) = 15 ---------- Eqn.(1)

Also,

→ Distance covered = xy = 540km .

→ xy = 540km .

→ y = (540/x). ----------- Eqn.(2)

Putting value of Eqn.(2) in Eqn.(1) Now,

→ 5(540/x) - x = 15

→ (2700 - x²)/x = 15

→ 2700 - x² = 15x

→ x² + 15x - 2700 = 0

→ x² +60x - 45x - 2700 = 0

→ x(x + 60) - 45(x + 60) = 0

→ (x + 60)(x - 45) = 0

→ x = (-60) or 45 km/h . [ Speed in negative ≠ ] .

Therefore,

→ Speed of Passenger Train = 45km/h .

→ Time taken by Passenger Train to reach Mid - route = y Hours = (540/x) = (540/45) = 12 Hours.

Hence,

→ Exact Time Passenger Train reach at Mid - route = 6PM + 12 Hours. = 6AM (Ans.)

∴ Both Trains meet each other at mid-route at 6AM.