Question

A train covers the first half of the distance be-
tween two stations at a speed of 40 km/hour the
other half at 60 km/hour. Then its average speed
is :​

Answer 1

Answer:

50 KM IS CORRECT

Explanation:

40+60KM ÷2

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 48 km/h

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$\huge\sf\blue{Given}$

✭ Speed₁ = 40 km/h

✭ Speed₂ = 60 km/h

✭ Speed₁ for half of the journey and the remaining half with Speed₂

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$\huge\sf\gray{To \:Find}$

◈ Average speed of the body?

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$\huge\sf\purple{Steps}$

Let's assume the distance as 2x

Case 1

• Speed = 40 km/h
• Distance = x

➝ $\underline{\underline{\sf Speed = \dfrac{Distance}{Time}}}$

➝ $\sf 40 = \dfrac{x}{Time}$

➝ $\sf \green{Time_1 = \dfrac{x}{40}}$

Case 2

• Speed = 60 km/h
• Distance = x

➳ $\underline{\underline{\sf Speed = \dfrac{Distance}{Time}}}$

➳ $\sf 60 = \dfrac{x}{Time}$

➳ $\sf \red{Time_2 = \dfrac{x}{60}}$

Average speed is given by,

$\underline{\boxed{\sf Avg \ Speed = \dfrac{Total \ D}{Total \ T}}}$

Substituting the values,

»» $\sf Avg \ Speed = \dfrac{Total \ D}{Total \ T}$

»» $\sf Avg \ Speed = \dfrac{2x}{\dfrac{x}{40} + \dfrac{x}{60}}$

»» $\sf Avg \ Speed = \dfrac{2x}{\dfrac{40x+60x}{40\times 60}}$

»» $\sf Avg \ Speed = \dfrac{2x}{\dfrac{100x}{2400}}$

»» $\sf Avg \ Speed = 2x \times \dfrac{2400}{100x}$

»» $\sf \orange{Avg \ Speed = 48 \ km/h}$

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