#
★ Quadratic Equations ★

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

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## Answers

__Answer:____-__

→ Speed of express train = **4****4**** ****km/****h**

→ Speed of passenger train = **3****3**** ****km/****h**

__Explanation____:____-__

Let the speed of the passenger train be **v ****km/****h.**

Thus, speed of the express train :-

**= (v + 11) km/****h**

Now, let's calculate the time taken by both the trains to travel between Mysore and Bangalore.

__Time taken by the passenger ____train__

= Distance/Speed

= [132/v] hrs

__Time ____taken ____by ____the ____express train __

= Distance/Speed

= [132/(v + 11)] hrs

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Now according to the question, we get the equation as :-

⇒ [132/v] - [132/(v + 11)] = 1

⇒ [132(v + 11) - 132v]/[v² + 11v] = 1

⇒ [1452 + 132v - 132v] = v² + 11v

⇒ 1452 = v² + 11v

⇒ v² + 11v - 1452 = 0

⇒ v² + 44v - 33v - 1452 = 0

⇒ v(v + 44) - 33(v + 44) = 0

⇒ (v - 33)(v + 44) = 0

__⇒ v = 33 km/h ; v = - 44 km/h__

But we know that speed cannot be negative.

So, speed of the passenger train :-

**= 33 km/h**

And, speed of the express train :-

= (33 + 11) km/h

**= 44 km/h**

__Given :-__

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

__To Find :-__

Average speed

__Solution :-__

Let's assume that average speed is x km

Now

Average speed = x + 11

According to the question

Cancel 132x from both sides

Either

x = 0 - 33

x = -33 km/h

or

x = 44 + 0

x = 44 km/h

Speed can't be negative so,

Speed of express train = 44 km/h

Speed of passenger train = 44 - 11 = 33 km/h