Question

A train travels a distance of 480km at a uniform speed . if the speed had been 8km/h less,then it would have taken 3hours more to cover the same distance .find the speed of the train.

Answer 1

Let take speed of the train = x km/hAnd time taken by train in normal speed  = y hoursA train travels a distance of 480 km at a uniform speed.Distance = speed  × timeSo we get x*y = 480                   …..(1).
 If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance
New speed  = x – 8 km/h
Time taken = y + 3 hours
Use same formula again
Distance = speed × time

or,  (x- 8) × (y + 3)  = 480   
 xy + 3x -8y – 24  = 480
plug xy = 480 we get  480 + 3x – 8y – 24   = 480
  3x – 8y – 24            = 0
Find the value of y here  
 -8y = 24 – 3x
Divide by – 8 we gety = -3 + 3/8x
Plug this value in equation first we get
x(-3 + 3/8x) = 480-3x + 3/8 
x2 = 480
Multiply by 8 we get-24 x +  3x2 = 3840
Divide by 3 we getx2 – 8x  = 1280x2 – 8x  - 1280 =0

Answer 2

$\huge\sf{Let,}$

$\large\sf{speed\:of\:train=x\:km/h}$

$\large\sf{time=\frac{480}{x}hr.}$

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$\huge\sf{In\:2nd\:condition}$

$\large\sf{speed=(x-8)km/h}$

$\large\sf{time=3hrs.}$

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$\large\sf{time\:to\:travel\:480km=(\frac{480}{x}+3)hrs.}$

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$\large\sf{speed×time=distance}$

$\large\sf{(x-8)×( \frac{480}{x} + 3) = 480}$

$\large\sf{480 + 3x - \frac{3840}{x} = 24}$

$\large\sf{3x - \frac{3840}{x} = 24}$

$\large\sf{{3x}^{2} - 24x - 3840 = 0}$

$\large\sf{{x}^{2}-8x-1280=0}$