Name: Problem Based on Formation of Quadratic Equation
Uploaded: 2019-07-19
Duration: 5 min 41 s
Description: In this video, we will learn to solve a problem from the chapter Quadratic Equations, where we need to form an equation whose roots are given. Let's watch an...

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 / hr

more. Find the original speed of the train .

Accepted Answer

Let the original speed of the train be $x$ km/hr
If the speed is increased by $5$ km/hr then, the the will be $(x + 5)$ km/hr
Distance to be travelled is $360$ km.

$Speed = \frac{Distance travelled}{Time taken}$
Time taken by the train to travel $360$ km at a speed of $x$ km/hr is = $\frac{360}{x}$
Time taken by the train to travel $360$ km at a speed of $(x + 5)$ km/hr is = $\frac{360}{x + 5}$
Time taken by the train to travel $360$ km will take $48$ min less if its speed is increased to $(x + 5)$ km/hr

Since speeds are in km/hr, we convert $48$ minutes into hours
$\Rightarrow 48$ minutes $= \frac{48}{60} = \frac{8}{10}$ hr
$\Rightarrow \frac{360}{x} - \frac{360}{x + 5} = \frac{8}{10}$
$\Rightarrow \frac{1}{x} - \frac{1}{x + 5} = 450$
$48 minutes$
$\Rightarrow 2250 = x^{2} + 5 x$

$\Rightarrow x^{2} + 5 x - 2250 = 0$
$\Rightarrow x^{2} + 50 x - 45 x - 2250 = 0$
$\Rightarrow x (x + 50) - 45 (x + 50) = 0$
$\Rightarrow (x - 45) (x + 50) = 0$
$\Rightarrow (x - 45) = 0$ or $x + 50 = 0$
$\Rightarrow x = 45, - 50$

Speed of the train cannot be negative.

Hence, the original speed of the train is $45$ km/hr.

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 $5 km / hr$ more. Find the original speed of the train .

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

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/hr more. Find the original speed of the train .

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

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 $5 km / hr$ more. Find the original speed of the train .