A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less,

Question

Reprsent the following situations 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

Let the initial speed of a train be ‘x’ km/h. 

Time required to travel x km is 1 hour. 

Time required to travel 480 km ………? 

\(\frac{480}{x}\)hr 

If its speed decreases to 8 km/h, then it is (x – 8) km/h. 

Time required to cover (x – 8) km is 1 Hr. 

Time required to cover 480 km ………..?

∴ x(3x + 456) = 480 (x – 8) 

3x² + 456x = 480x + 3840 

3x² + 456x – 480 x + 3840 = 0 

3x² – 24x + 3840 = 0 

∴ x² – 8x + 1280 = 0 

This is the required equation. 

Now, we have to solve for x :

x² – 8x + 1280 = 0 

x² – 40x + 32x + 1280 = 0 

x(x – 40) + 32(x + 40) = 0 

(x – 40) (x + 32) = 0 

If x – 40 = 0, then x = 40 

If x + 32 = 0, then x = -32 

∴ Average speed of train is 40 km/hr.