Question

A train travels a certain speed for a distance of 63 km and then travels a distance 72 at an average 6 / h more than it's original speed . If it takes 3 hrs to complete total journey, what is the original average speed?

Answer 1

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✓✓A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed, If it takes 3 hours to complete total journey, what is its original average speed?

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Let original average speed of train be x km/hr

Time taken to covered 63 km $\bf\:=\dfrac{63}{x}$

Again, speed of train = ( x + 6 ) km/hr

Time taken to Covered 72 km$\bf\:=\dfrac{72}{x+6}$

A/Q,

$\bf\dfrac{63}{x}+\dfrac{72}{x+6}=3$

$\bf\implies\dfrac{21}{x}+\dfrac{24}{x+6}=1$

$\bf\implies\dfrac{21x+126+24x}{x^2+6x}=1$

$\bf\implies\:45x+126={x}^{2}+6x$

$\bf\implies\:{x}^{2}-39x-126=0$

$\bf\implies\:{x}^{2}-42x+3x-126=0$

$\bf\implies\:x(x-42)+3(x-42)=0$

$\bf\implies\:(x-42)\:(x+3)=0$

then,

$\bf\implies\:x-42=0\:or\:x+3=0$

$\bf\implies\:x=42\:or\:x=-3$

Therefore, Speed cannot be negative .

so, The original average speed of train is 42 km/hr.