Question

Distance between two stations x and y is 778 km. A train covers the journey from x to y at the speed of 84 kmph and returns to x with the speed of 56 kmph. Find the average speed of the train (in kmph) for the whole journey.​

Answer 1

$\color{grey}\underline{ \rm \large \: \: Question :- }$

Distance between two stations x and y is 778 km. A train covers the journey from x to y at the speed of 84 kmph and returns to x with the speed of 56 kmph. Find the average speed of the train (in kmph) for the whole journey.

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$\color{grey}\underline{ \rm \large \: \: Given :- }$

• Distance between two stations [x and y] = 778 km

• train covers the journey from x to y at the speed = 84 km/hr

• Then train returns to x with the speed = 56 km/ph

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$\color{grey}\underline{ \rm \large \: \: To \: Find :- }$

• The average speed of the train .

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$\color{grey}\underline{ \rm \large \: \: Formula \: Used:- }$

$\: \: \: \: \boxed{ \blue{ \sf \star \: \: avarage \: speed = \dfrac{2}{ \dfrac{1}{x} + \dfrac{1}{y} } }}$

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$\color{grey}\underline{ \rm \large \: \: Step \: By \: Step \: Solution:- }$

Let's find the answer by applying the formula of avarage speed

$\: \: \: \: \: { \sf : \longrightarrow \: \: avarage \: speed = \dfrac{2}{ \dfrac{1}{x} + \dfrac{1}{y} } }$

$\: \: \: \:{ \sf : \longrightarrow\: \: avarage \: speed = \dfrac{2xy}{x + y} }$

• x = 84
• y = 56

$\: \: \: \:{ \sf : \longrightarrow\: \: avarage \: speed = \dfrac{2 \times 84 \times 56}{84+ 56} }$

$\: \: \: \:{ \sf : \longrightarrow\: \: avarage \: speed = \dfrac{2 \times \cancel{84} \times 56}{ \cancel{140}} }$

$\: \: \: \:{ \sf : \longrightarrow\: \: avarage \: speed = \dfrac{2 \times 21\times 56}{ 35} }$

$\: \: \: \:{ \sf : \longrightarrow\: \: avarage \: speed = \dfrac{2 \times 3\times 56}{ 5} }$

$\: \: \: \:{ \sf : \longrightarrow\: \: avarage \: speed = \dfrac{ 336}{ 5} }$

$\: \: \: \:{ \sf : \Longrightarrow\: \: avarage \: speed = \red{ 67.2 \: km/hr} }$

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$\color{grey}\underline{ \rm \large \: \: Answer :- }$

$\: \: \: \:{ \sf \: \: avarage \: speed = \green{ 67.2 \: km/hr} }$

Answer 2

The required average speed given by the formula,

Average speed=(2xy/x+y)km/hr

Where,

• x=84 kmph
• y=56kmph

Average speed= 2×84×56/84+56

=67.2kmph