Question

A train travels at a certain average speed for a distance of 63 km and then Travels at a distance of 72 km at an average speed of 6 km more than its original speed if it takes 3 hours to complete total jaldi what is the average speed

Answer 1

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$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,
Distance $S_{1} = 63\: km$

Let Average Speed $S_{1} =x\: kmph$

Distance $S_{2} = 72\: km$

Average Speed $S_{1} =(x+6)\: kmph$

Time taken by the train for whole Journey $t = 3\: Hrs$

Average Speed = ?

$\underline{\huge{\textsf{Step-1:}}}$
Express the time taken by train in covering 63 km and 72 km in terms of Average speed

We have,
$time\: taken = \dfrac{Distance\: Covered}{Speed}$

$\implies t_{1} = \dfrac{63}{x}$

$\implies t_{2} = \dfrac{72}{(x+6)}$


$\underline{\huge{\textsf{Step-2:}}}$
Find the time taken for whole Journey.

$time\: taken\: for\: the\: whole\: journey = t_{1} + t_{2}$


$time\: taken\: for\: the\: whole\: journey = \dfrac{63}{x} + \dfrac{72}{x+6}$


$\underline{\huge{\textsf{Step-3:}}}$
Solve to obtain the equation in variable by substituting t = 3

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

$\implies \dfrac{63(x+6)+72(x)}{x(x+6)} = 3$

$\implies 63(x+6)+72(x) = 3x(x+6)$

$\implies 63x+278+72x = 3x^{2}+18x$

$\implies 3x^{2}+18x-135x-378= 0$

$\implies 3x^{2}-117x-378= 0$


$\underline{\huge{\textsf{Step- 4}}}$
Factorise the Obtained equation and solve for the value of the variable.

$3x^{2}-117x-378= 0$

$\implies 3x^{2}-9x+126x-378= 0$

$\implies 3x(x+3)-126(x+3)= 0$

$\implies (3x-126)\, (x+3) = 0$

$\therefore$
$3x-126 = 0$

$3x = 126$

$x = 42\: kmph$

while equating (x+3) to zero, Negative value will be obtained

But Speed can't be Negative

So Average Speed of the train = $\underline{42\: kmph}$

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