Name: Nature of the Roots: Illustration
Uploaded: 2019-07-19
Duration: 2 min 4 s
Description: We cannot judge a book by its cover, but we can find the nature of the roots of a given quadratic equation without finding roots. Let's learn just how we can...

Question

An express train takes

1

hour less than a passenger train to travel

132 k m

between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is

11 k m / h

more than that of the passenger train, find the average speed of the two trains.

Accepted Answer

Let the average speed of passenger train $b e x km / h .$

Average speed of express train $= (x + 11) km / h$ (Given in question)

According to the question, the time taken by the express train to cover $132 km$ is $1$ hour less than a passenger train.

Therefore, time taken by passenger train – time taken by express train $= 1$ hour

$∴ \frac{132}{x} - \frac{132}{x + 11} = 1$ $(T o t a l t i m e = \frac{D i s t a n c e}{A v e r a g e S p e e d})$

$\Rightarrow 132 [\frac{x + 11 - x}{x (x + 11)}] = 1$

$\Rightarrow \frac{132 \times 11}{x (x + 11)} = 1$

$\Rightarrow 132 \times 11 = x (x + 11)$

$\Rightarrow x^{2} + 11 x - 1452 = 0$

$\Rightarrow x^{2} + 44 x - 33 x - 1452 = 0$

$\Rightarrow x (x + 44) - 33 (x + 44) = 0$

$\Rightarrow (x + 44) (x - 33) = 0$

$\Rightarrow x = - 44, 33$

Average speed of passenger train cannot be negative. Hence, the speed of the passenger train is $33 km / h$ and thus, the speed of the express train will be $33 + 11 = 44 k m / h$ .

Important Questions on Quadratic Equations

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