Question

A passanger train takes 2 hours more than express train to travel 240 kmthe speed of express train is more than passanger tain by 10 km then find the speed of both the tra

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• A passenger train takes 2 hours more than express train to travel 240 km

• The speed of express train is more than passenger train by 10 km/hr

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Speed of both the trains

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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• Let the speed of passenger train be "p"

• Let the speed of express train be "e"

• Let time taken by passenger train be "T1"

• Let time time by express train be "T2"

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We know that ,

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➠ $\sf T = \dfrac { D } { S}$ ⚊⚊⚊⚊ ⓵

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Where ,

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• S = Speed

• D = Distance

• T = Time taken

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$\underline{\bold{\texttt{For passenger train :}}}$

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• S = p

• D = 240

• T = T1

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf T = \dfrac { D } { S}$

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➜ $\sf T1 = \dfrac { 240} { p}$ ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{For express train :}}}$

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• S = e

• D = 240

• T = T2

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf T = \dfrac { D } { S}$

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➜ $\sf T2 = \dfrac { 240} { e}$ ⚊⚊⚊⚊ ⓷

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Given that , passenger train takes 2 hours more than express train to travel 240 km

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Thus ,

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➜ T1 = T2 + 2

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⟮ From ⓶ & ⓷ ⟯

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➜ $\sf \dfrac { 240} { p} = \dfrac { 240} { e} + 2$ ⚊⚊⚊⚊ ⓸

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Also given that the speed of express train is more than passenger train by 10 km/hr

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So,

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➜ e = p + 10 ⚊⚊⚊⚊ ⓹

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⟮ Putting the e = p + 10 from ⓹ to ⓸ ⟯

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➜ $\sf \dfrac { 240} { p} = \dfrac { 240} { e} + 2$

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➜ $\sf \dfrac { 240} { p} = \dfrac { 240} {p + 10} + 2$

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➜ $\sf \dfrac { 240 } { p } = \dfrac { 240 + 2p + 20 } { p + 10 }$

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➜ $\sf \dfrac { 240 } { p } = \dfrac { 260 + 2p } { p + 10 }$

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➜ 240(p + 10) = p(260 + 2p)

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➜ 240p + 2400 = 260p + 2p²

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➜ 2p² + 260p - 240p - 2400 = 0

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➜ 2p² + 20p - 2400 = 0

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⟮ Dividing the above equation by 2 ⟯

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➜ p² + 10p - 1200 = 0

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Here we got a quadratic equation so let us solve it by splitting the middle term method

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➜ p² + 40p - 30p - 1200 = 0

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➜ p(p + 40) -30(p + 40) = 0

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➜ (p + 40)(p - 30) = 0

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• p = -40
• p = 30

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As speed can't be negative hence

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➨ p = 30 ⚊⚊⚊⚊ ⓺

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• Hence the speed of passenger train is 30 km/hr

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⟮ Putting p = 30 from ⓺ to ⓹ ⟯

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➜ e = p + 10

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➜ e = 30 + 10

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➨ e = 40

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• Hence the speed of express train is 40 km/hr

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