An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. find the average speed of express train.

Question

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.

Answer 1

Given: An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/hr more than that of the passenger train.

To find: the quadratic equation to find the average speed of express train.

Solution: Let the average speed of passenger train be ‘x’ km/hr and the time taken by passenger train be ‘t’ hr.

Since an express train takes 1 hour less than a passenger train and the average speed of the express train is 11 km/hr more than that of the passenger train.

So, For the express train average speed = x + 11, time taken = t - 1

Since,Distance = speed × time

Given, total distance traveled = 132 kmFor passenger train:

⇒ x × t = 132

⇒ t = 132/x ...... (1)

Also for express train (x + 11) × (t - 1) = 132 

Substitute the value of t from (1),

⇒ (x + 11)(132-x) = 132x 

⇒ 132x - x² +1452 -11x = 132x 

⇒ - x² -11x +1452 = 0 

⇒ x² + 11x – 1452 = 0 

Required quadratic equation

Comments

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