Question

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Answer 1

Given : A train can finish a journey in 10 hrs travelling at a speed of 56 km/hr . If another faster train is to cover the same journey in 8 hrs .

Need To Find : Speed of new train .

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❍ First find the distance that covered by both train using the values given for speed and Distance of first train :

$\underline {\frak{\dag As , \: We \: know \:that \::}}$

⠀⠀⠀⠀⠀$\underline {\boxed { \sf{\star Distance = Speed \times Time }}}$

⠀⠀⠀⠀⠀ Here Speed is in the km/hr and the time is in hours.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \:of\:Train_{1} \::}}$

$\qquad \qquad \qquad:\implies \sf { Distance = 56 \times 10 }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm { Distance = 560\: km}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Distance \:travel \:by\:both \:trains\:is\:560 km}}}$

Given that ,

• Train 2 have to cover same journey then the Distance will be same :

Then ,

• Distance travelled by Train 2 = 560 km.

• Time taken to cover Distance is = 8 hrs . [ Given that ]

❒ Finding Speed of Train 2 :

$\underline {\frak{\dag As , \: We \: know \:that \::}}$

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

⠀⠀⠀⠀⠀ Here Distance is in the km and the time is in hours.

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \:of\:Train_{1} \::}}$

$\qquad \qquad \qquad:\implies \sf { Speed = \dfrac{560}{8}}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm { Speed _ {(Train _{2}} = \: 70\:km/hr}}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence ,\: Speed \:of \:new\: \:train\:to\:cover\:same\:journey \:is\:\bf{70 km/hr}}}}$

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