Question

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

The original speed of the train is 40 km/hour

Step-by-step explanation:

Let the original speed of the train be x km/hour

Distance traveled by the train = 480 km

\begin{gathered}\text{Time taken by train = }\frac{480}{x}\\\\\text{If the train would have taken 3 hours more then time = }\frac{480}{x-8}\\\\\implies \frac{480}{x}=\frac{480}{x-8}+3\\\\\implies \frac{480}{x}-\frac{480}{x-8}=3\\\\\implies 3x^2-24x+3840=0\\\\\implies x^2-8x+1280=0\\\\\implies \text{ x = -32 or x = 40}\\\\\text{But speed can not be negative }\implies x=40\end{gathered}

Time taken by train =

x

480

If the train would have taken 3 hours more then time =

x−8

480

⟹

x

480

=

x−8

480

+3

⟹

x

480

−

x−8

480

=3

⟹3x

2

−24x+3840=0

⟹x

2

−8x+1280=0

⟹ x = -32 or x = 40

But speed can not be negative ⟹x=40

Hence, the original speed of the train is 40 km/hour

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Answer 2

Answer:

Step-by-step explanation:

Let the speed of the train be x km/hr. Then

Time taken to travel a distance of 480 km = $\frac{480}{x}$hr

Time taken by the train to travel a distance of 480 km with the speed (x−8) km/hr = $\frac{480}{x - 8} hr$

It is given that if the speed had been 8 km/hr less, then the train would have taken 3 hours more to cover the same distance

∴ $\frac{480}{x - 8} = \frac{480}{x} + 3$

⇒$\frac{480}{x- 8} - \frac{480}{x} = 3$ ⇒$\frac{480(x -x+8)}{x(x-8 )} = 3$ ⇒ $\frac{480 * 8}{x (x - 8)} = 3$

 $3x (x-8)=480 * 8$⇒$x(x - 8)=160 * 8$⇒$x^{2} - 8x -1280 = 0$

This is the required quadratic equation.