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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 − 8 x − 1280 = 0

b

x 2 − 8 x + 1280 = 0

c

x 2 + 8 x − 1280 = 0

d

x 2 + 8 x + 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,

T i m e = D i s t a n c e S p e e d

Time taken by train to cover 480 km distance is,

⇒ D i s t a n c e S p e e d

⇒ 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,

T i m e = D i s t a n c e S p e e d

⇒ 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 + 3 x x − 8

⇒ 480 x = 480 x − 8 + 3 x x − 8

⇒ 480 x = 480 x − 3840 + 3 x 2 − 24 x

Take the left term to the right side of the equation.

⇒ 3 x 2 − 24 x + 480 x − 480 x − 3840 = 0

⇒ 3 x 2 − 24 x − 3840 = 0 ⇒ 3 (x 2 − 8 x − 1280) = 0

⇒ x 2 − 8 x − 1280 = 0

The given situation is represented by the quadratic equation

x 2 − 8 x − 1280 = 0

.
Hence, option 1 is correct.

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