Question

The distance between two station is 500 kmA train goes from one station to the other with the speed of 50 km/hr and return from a speed of 25 km/hr what is is the avrage speed of the train during the journey​​

Answer 1

✯ ᴀɴsᴡᴇʀ ✯

★ given →

☞︎︎︎ distance between two station,(s) = 500km

☞︎︎︎ speed of train during first journey,(v1) = 50km/hr

☞︎︎︎ speed of train during second journey,(v2)= 25km/hr

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★ to find →

☞︎︎︎ average speed of the train during the journey?

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★ solution →

we know that,

$\bold{\star speed = \frac{distance}{time} } \: \: \: \: \\ \\ \implies \bold{time = \frac{distance}{sped} } \:$

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・time taken during first trip(t1) ;

$\: \: \: \: \: \: \: \: \bold{ \star \: \: t1 = \frac{s}{v1} } \: \\ \\ : \implies \bold{t1 = \frac{500}{50} } \\ \\ : \implies \bold{ t1 = 10hr}$

・time taken during second trip(t2);

$\: \: \: \: \: \: \: \: \: \: \bold{ \star \: t2 = \frac{s}{v2} } \\ \\ : \implies \bold{t2 = \frac{500}{25} } \\ \\ : \implies \bold{t2 = 20hr}$

☆ total time taken during the journey,(t)

$\: \: \: \: \: \: \: \: \: \: \: \: \bold{t = t1 + t2} \\ \\ : \implies \bold{t = 10 + 20} \\ \\ : \implies \bold{\: t = 30hr \: \: \: \: } \:$

☆ total distance covered by train during the journey, (S);

$\: \: \bold{S = s + s} \\ \\ : \implies \bold{S = 500 + 500} \\ \\ :\implies \bold{S = 1000km} \: \: \: \:$

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➪ for finding average speed of the train,we have,

・total time taken(t) = 30km

・total distance covered(S) = 1000km

and we know that,

$\bold{ \tt \: average \: speed = \frac{total \: distance}{total \: time} } \: \: \: \: \\ \\ : \implies \bold{Vab = \frac{S}{t} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \: \bold{Vab = \frac{1000}{30} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \: \bold{Vab = \frac{100}{3} kmh ^{ - 1} } \: \: \: \: \:$

hence, average speed of the train during the journey is 100/3 km/hr or 33.34km/hr