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# A Train Travels at a Certain Average Speed for a Distance 63 Km and Then Travels a Distance of 72 Km at an Average Speed of 6 Km/Hr More than the Original Speed, If It Takes 3 Hours to - CBSE Class 10 - Mathematics

ConceptSituational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated

#### Question

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed, If it takes 3 hours to complete total journey, what is its original average speed?

#### Solution

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

Time taken to cover 63 \text { km } = 63/xx hours

Time taken to cover 72 km when the speed is increased by 6 (km) /(hr) = 72/(x + 6) hours

According to given information, we have

63/ xx + 72/(x + 6) = 3

⇒21/x + 24/(x +6) = 1

⇒ (21x + 126 + 24x)/(x^2 + 6x) = 1

⇒ 45x + 126 = x^2 + 6x

⇒x^2 - 39x - 126 = 0

⇒ x^2 - 42x + 3x - 126 = 0

⇒ x(x - 42) + 3(x - 42) = 0

Since the speed cannot be negative, x ≠-3

⇒ (x - 42)(x + 3) = 0

⇒ x-42 =0 or x + 3 = 0

⇒ x = 42

Thus, the original average speed of the train is 42 km/hr.

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Solution A Train Travels at a Certain Average Speed for a Distance 63 Km and Then Travels a Distance of 72 Km at an Average Speed of 6 Km/Hr More than the Original Speed, If It Takes 3 Hours to Concept: Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated.
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