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.What is the speed of the train?

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Answer 1

$\huge\bold{Answer:}$

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

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

$\sf\color{red}Hence,\: the\: original\: speed \:of \:the \:train \:is\: 40\: km/hour$

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Answer 2

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Let us consider:-

→ Speed of train = x km/h

→Time taken to travel 480 km = 480 (x) km/h

→ In second case, the speed of train = (x – 8) km/h

Given:-

→ The train will take 3 hours to cover the same distance.

→ Therefore, time taken to travel 480 km = 480x + 3 km/h

We know that:-

→ Speed × Time = Distance

Therefore,

→ (x – 8)(480/x + 3) = 480

→ 480 + 3x – 3840/x – 24 = 480

→ 3x – 3840/x = 24

→ 3x² – 8x – 1280 = 0

Hence, 3x² – 8x – 1280 = 0 is the required equation.