Question

Represent the following situation in the form of quadratic equations :
A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Answer 1

Sorry, for bad handwriting

Answer 2

Answer:

Speed of the train = 40km/hr

Step-by-step explanation:

Distance ( d ) = 480 km

[ Speed ( s ) = distance/time

=> d = s/t ]

Let the speed of train by traveling

with speed of x km/hr

( t1 )= 480/x -----( 1 )

Time taken , If train travel with

8 km/hr less speed

( t2 ) = 480/(x-8) ----- ( 2 )

From the given problem ,

t2 - t1 = 3 hours

=> 480/( x - 8 ) - 480/x = 3

[ From ( 1 ) and ( 2 ) ]

=>[480x-480(x-8)]/[x(x-8)] = 3

=> 480( x - x + 8 ) = 3x(x-8)

=> 160 × 8 = x² - 8x

=> 1280 = x² - 8x

=> x² - 8x - 1280 = 0

=> x² - 40x + 32x - 1280 = 0

=> x( x - 40 ) + 32 ( x - 40 ) = 0

=> ( x - 40 )( x + 32 ) = 0

=> x - 40 = 0 or x + 32 = 0

=> x = 40 or x = -32

Therefore ,

x = 40 ( x > 0 )

Speed of the train ( x ) = 40km/hr

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