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Question

(A) Let the speed of the faster train be $x\, km/hr$. Then the speed of the slower train is $(x - 20)\, km/hr$.The time taken by the faster train is $

Vedclass · Accepted Answer

$80\, km/hr$

Vedclass · Answer

(A) Let the speed of the faster train be $x\, km/hr$. Then the speed of the slower train is $(x - 20)\, km/hr$.The time taken by the faster train is $T_1 = \frac{400}{x}$ hours.The time taken by the slower train is $T_2 = \frac{400}{x - 20}$ hours.According to the problem,the faster train takes $1$ hour less than the slower train,so $T_2 - T_1 = 1$.$\frac{400}{x - 20} - \frac{400}{x} = 1$$400 \left( \frac{x - (x - 20)}{x(x - 20)} ight) = 1$$400 	imes 20 = x^2 - 20x$$x^2 - 20x - 8000 = 0$$(x - 100)(x + 80) = 0$Since speed cannot be negative,$x = 100\, km/hr$.The speed of the slower train is $x - 20 = 100 - 20 = 80\, km/hr$.

The faster train takes $1$ hour less than the slower train for covering a $400\, km$ distance. If the speed of the slower train is $20\, km/hr$ less than the speed of the faster train,find the speed of the slower train.

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