Question

A train, travelling at a uniform speed for $360$ km, would have taken $48$ minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train in km/hr.

Answer 1

Let $x=$ Original Speed

we know that $\frac{distance}{speed}=time$

So as per the question the following equation can be formed

$\frac{360}{x}-\frac{360}{x+5}=\frac{48}{60}$ [1 hour = 60 minutes]

$\Rightarrow \frac{1}{x}-\frac{1}{x+5}=\frac{48}{60}\cdot \frac{1}{360}$

$\Rightarrow \frac{5}{x^2+5x}=\frac{1}{450}$

$\Rightarrow x^2+5x-2250=0$

$\Rightarrow x^2-45x+50x-2250=0$

$\Rightarrow x(x-45)+50(x-45)=0$

$\Rightarrow (x-45)(x+50)=0$

$x=45,-50$

As the speed can't be negative so,

$x=45$