Question

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Answer 1

$\huge\sf\pink{Answer}$

☞ Speed of Express train = 33 km/h

☞ Speed of Passenger train = 44 km/h

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$\huge\sf\blue{Given}$

✭ A train takes 1 hour less than a passenger train

✭ Distance = 132 km

✭ Average speed of express train is 11 km/h more than the passenger train

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$\huge\sf\gray{To \:Find}$

◈ The Average speed of two trains?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

➢ Speed of express train = x

➢ Speed of passenger train = (x+11)

So we know that the formula to find speed is given by

$\underline{\boxed{\red{\sf Speed = \dfrac{Distance}{Time}}}}$

So then,

$\sf Time = \dfrac{distance}{speed}$

For convenience let Express train be ET and Passenger train be PT

»» $\sf Time \ by \ EP = \dfrac{132}{x}$

»» $\sf Time \ by \ PT = \dfrac{132}{(x+11)}$

As the Difference in time is 1 hour

➳ $\sf\dfrac{132}{x}-\dfrac{132}{x+11} = 1$

➳ $\sf 132(x+11)-132x = x(x+11)$

➳ $\sf 132x +1452-132x = x^2 +11x$

➳ $\sf x^2 + 11x-1452 = 0$

Using Middle term splitting

➝ $\sf x^2+44x-33x-1452=0$

➝ $\sf x(x+44) -33(x+44) = 0$

➝ $\sf (x+44)(x-33) = 0$

➝ $\sf x = 33 \ or \ -44$

So ignoring negatively

➝ $\orange{\sf x = 33}$

Substituting the value of x

➠ Speed of Express train = 33km/hr

➠ Speed of Passenger train = (x+11) = 44km/hr

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