Question

A train travels at a certain average speed for a distance of 54 km and then Travels a distance of 63 km at an average speed of 6 km per hour more than the first speed if it takes 3 hours to complete the total churning what is its first speed

Answer 1

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Answer 2

Solution

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Distance =54 km

Let the average speed be x

Distance =63 km

The average speed to cover this distance =x+6

Total time taken =3 hr

t=

S

D

∴

x

54

+

x+6

63

=3

⇒

x(x+6)

54(x+6)+63x

=3

⇒54x+324+63x=3x

2

+18x

⇒3x

2

−99x−324=0

⇒x

2

−33x−108=0

⇒x

2

−36x+3x−108=0

⇒x(x−36)+3(x−36)=0

⇒(x−36)(x+3)=0

Then x=36 and x=−3

x=−3 is not admissible because it is negative

Then x=36

So speed =36 km/hr