An express train takes 1, hour less than a pa | vedclass

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Question

(A) Let the average speed of the passenger train be $x\, km/h$.Average speed of the express train $= (x + 11)\, km/h$.Time taken by the passenger trai

Vedclass · Accepted Answer

$33, 44$

Vedclass · Answer

(A) Let the average speed of the passenger train be $x\, km/h$.Average speed of the express train $= (x + 11)\, km/h$.Time taken by the passenger train to cover $132\, km = \frac{132}{x}\, hours$.Time taken by the express train to cover $132\, km = \frac{132}{x + 11}\, hours$.According to the problem,the express train takes $1\, hour$ less than the passenger train:$\frac{132}{x} - \frac{132}{x + 11} = 1$$132 \left[ \frac{x + 11 - x}{x(x + 11)} ight] = 1$$\frac{132 	imes 11}{x^2 + 11x} = 1$$x^2 + 11x = 1452$$x^2 + 11x - 1452 = 0$Solving the quadratic equation by splitting the middle term:$x^2 + 44x - 33x - 1452 = 0$$x(x + 44) - 33(x + 44) = 0$$(x + 44)(x - 33) = 0$$x = -44$ or $x = 33$.Since speed cannot be negative,$x = 33\, km/h$.Therefore,the speed of the passenger train is $33\, km/h$ and the speed of the express train is $33 + 11 = 44\, km/h$.

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