Question

A train travels a distance of 480 km at a uniform speed if the speed had been 8km/hr more,then it would have taken2 hours less to cover the same distance.find the speed of the train

Answer 1

Step-by-step explanation:

Answer:

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{lgathered}\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{lgathered}

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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