Question

Please help Explain step by step please ​

Answer 1

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A. T. Q

Speed of express train = x km/h

Speed of Ordinary train = (x - 12) km/h

Distance covered by both trains = 240 km

● it is given that ordinary train take 1 hour more than express train to cover 240 km

So,

using formula

$\boxed{ \tt{time = \frac{distance}{speed} }}$

$\implies\mathrm{ \frac{240}{x - 12} - \frac{240}{x} = 1 }$

Taking LCM

$\implies \mathrm{ \frac{240x - 240x + 240(12)}{ {x}^{2} - 12x} = 1 }$

cross multiplying

$\implies \mathrm{240(12) = {x}^{2} - 12x }$

$\implies \mathrm{ {x}^{2} - 12x - 2880 = 0 }$

splitting middle term

$\implies \mathrm{ {x}^{2} - 60x + 48x - 2880 = 0}$

$\implies \mathrm{x(x - 60) + 48(x - 60) = 0}$

$\implies \mathrm{(x + 48)(x - 60) = 0}$

From here we will get

x = -48

and x = 60

Since,

speed can't be negative

Hence,

Speed of express train = 60 km/ h.

Answer 2

A. T. Q

Speed of express train = x km/h

Speed of Ordinary train = (x - 12) km/h

Distance covered by both trains = 240 km

● it is given that ordinary train take 1 hour more than express train to cover 240 km

So,

using formula

\boxed{ \tt{time = \frac{distance}{speed} }}time=speeddistance

\implies\mathrm{ \frac{240}{x - 12} - \frac{240}{x} = 1 }⟹x−12240−x240=1

Taking LCM

\implies \mathrm{ \frac{240x - 240x + 240(12)}{ {x}^{2} - 12x} = 1 }⟹x2−12x240x−240x+240(12)=1

cross multiplying

\implies \mathrm{240(12) = {x}^{2} - 12x }⟹240(12)=x2−12x

\implies \mathrm{ {x}^{2} - 12x - 2880 = 0 }⟹x2−12x−2880=0

splitting middle term

\implies \mathrm{ {x}^{2} - 60x + 48x - 2880 = 0}⟹x2−60x+48x−2880=0

\implies \mathrm{x(x - 60) + 48(x - 60) = 0}⟹x(x−60)+48(x−60)=0

\implies \mathrm{(x + 48)(x - 60) = 0}⟹(x+48)(x−60)=0

From here we will get

x = -48

and x = 60

Since,

speed can't be negative

Hence,

Speed of express train = 60 km/ h.