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Q.



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. Which of the following is the quadratic equation for the given statement?

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a

x 2 −8x−1280=0  

b

x 2 −8x+1280=0  

c

x 2 +8x−1280=0  

d

x 2 +8x+1280=0   

answer is A.

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Detailed Solution

Given that 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.
Let the speed of the train be x km/h.
Distance traveled by train at the uniform speed = 480 km.
We know,
Time= Distance Speed  
Time taken by train to cover 480 km distance is,
⇒ Distance Speed  
⇒ 480 x  h  
Since it took three hours more to cover 480 km at the speed of (x – 8) km/h, the time is,
⇒ 480 x  + 3 h  ….(1)
But,
Time= Distance Speed  
⇒ 480 x−8  ….(2)
The equations (1) and (2) are equal.
⇒ 480 x−8 = 480 x +3  
Convert the algebraic form into a standard form of quadratic equation.
Multiply both sides by x x−8  .
We get,
  ⇒x x−8 480 x−8 =x x−8 480 x +3x x−8  
⇒480x=480 x−8 +3x x−8  
⇒480x=480x−3840+3 x 2 −24x  
Take the left term to the right side of the equation.
⇒3 x 2 −24x+480x−480x−3840=0  
⇒3 x 2 −24x−3840=0 ⇒3( x 2 −8x−1280)=0  
⇒ x 2 −8x−1280=0  
The given situation is represented by the quadratic equation x 2 −8x−1280=0  .
Hence, option 1 is correct.
 
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