Question

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/hr more than that of the passenger train, find the average speed of two trains.

Answer 1

SOLUTION :

Given : Distance between Mysore and Bangalore = 132 km

Let the average speed of the passenger train be 'x' km/hr .

Average speed of the express train =  (x + 11) km/hr

Time taken by passenger train to cover 132 km = 132/x hr

[Speed = Distance/Time]

Time taken by the express train to cover 132 km = 132/(x+11) hr

A.T.Q  

132/(x+11) = (132/x) - 1

[Given: Time taken by the express train to cover the distance of 132 km is 1 hour less than the passenger train to cover the same distance]

(132/x) - 132/(x+11) = 1

[132(x +11) - 132(x)] / x(x+11) = 1  

[132x + 1452 - 132x] / x² + 11x = 1  

1452/x² + 11x = 1  

1452 = 1 × (x² + 11x)

x² + 11x = 1452  

x² + 11x - 1452 = 0  

By factorisation :  

x² + 11x - 1452 = 0

x² + 44x - 33x - 1452 = 0

x(x + 44) - 33(x + 44) = 0

(x - 33) (x + 44) = 0

x + 44 = 0  or  x - 33 = 0

x =  - 44 or x = 33

Since, speed can never be negative. So x ≠44 Therefore, x = 33  

speed of the passenger train = x = 33 km/h

speed of the express train = x + 11 = 33 + 11 = 44 km/h  

Hence, the speed of the passenger train is 33 km/hr and the speed of the express train   is 44 km/hr .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Hey mate,

Let the speed of passenger train be x km/hr 

Hence,

Speed of express train = (x +11) km/hr

Distance travelled by both the trains = 132 km 

Time taken = (Distance)/(Speed) 

Time taken by the passenger train = 132/x hrs 

Time taken by the express train = 132/(x + 11) hrs 

So ATQ,

132/x - 132/x+1 = 1

Just cross multiply and solve,

⇒ 132 × 11 = x(x + 11)

⇒ x^2 + 11x – 1452 = 0 

⇒ x^2 + 44x – 33x – 1452 = 0

⇒ x(x + 44) – 33(x + 44) = 0

⇒ (x + 44)(x – 33) = 0 

⇒ (x + 44) = 0

or (x – 33) = 0 ∴ x = –44

or x = 33 

Since speed cannot be negative, x = 3

Thus the sped of passenger train is 33 km/hr

and speed of express train is 44 km/hr. 

Hope this helps you out!