Question

a car travels 30 km at a uniform speed of 40 km per hour and next 30 km at a uniform speed of 20 km per hour find the average speed

Answer 1

GivEn:-

• A car travels 30 km at a uniform speed of 40 km per hour and next 30 km at a uniform speed of 20 km per hour.

To find:-

• The average speed of car

SoluTion:-

✩ Lets time taken by car = $\sf t_1\; and \;t_2$

As we know that,

${\underline{\boxed{\bf{\purple{Speed = \dfrac{Distance}{Time}}}}}}$

$\;\;\;\sf \star\;{\underline{\red{As\;per\;givEn\; Question\;:}}}$

★ Let's calculate Time from the first case,

Here,

• Distance ($\sf d_1$) = 30km

• Speed ($\sf S_1$) = 40km/h

✇ Now, Put the givEn values in above formula -

$\dashrightarrow\sf 40 = \dfrac{30}{t_1}$

$\dashrightarrow\sf t_1 = \cancel{ \dfrac{30}{40}}$

$\dashrightarrow{\underline{\boxed{\sf{\blue{t_2 = \dfrac{3}{4}\;hours}}}}}$ ★

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★ Let's calculate Time from the first case,

Here,

• Distance ($\sf d_2$) = 30km

• Speed ($\sf S_2$) = 20km/h

✇ Now, Put the givEn values in above formula -

$\dashrightarrow\sf 20 = \dfrac{30}{t_2}$

$\dashrightarrow\sf t_2 = \cancel{ \dfrac{30}{20}}$

$\dashrightarrow{\underline{\boxed{\sf{\blue{t_2 = \dfrac{3}{2}\;hours}}}}}$ ★

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★ Now, We have to calculate Average Speed of car,

As we know that,

${\underline{\boxed{\bf{\pink{Average\; Speed = \dfrac{Total\;Distance}{Total\;Time}}}}}}$

$\dashrightarrow\sf S_{avg} = \dfrac{ d_1 + d_2 }{ t_1 + t_2 }$

$\dashrightarrow\sf S_{avg} = \dfrac{30 + 30 }{ \frac{3}{4} + \frac{3}{2}}$

$\dashrightarrow\sf S_{avg} = \dfrac{60}{ \frac{3 + 6}{4}}$

$\dashrightarrow\sf S_{avg} = \dfrac{60}{ \frac{9}{4}}$

$\dashrightarrow\sf S_{avg} = \cancel{60} \times \dfrac{4}{ \cancel{9}}$

$\dashrightarrow\sf S_{avg} = 20 \times \dfrac{4}{3}$

$\dashrightarrow\sf S_{avg} = \dfrac{80}{3}$

$\dashrightarrow{\underline{\boxed{\sf{\orange{S_{avg} = 26.57\;km/h\;(approx)}}}}}$ ★

$\dag\;\sf \underline{Hence,\;Average\;Speed\;of\;car\;is\;26.57\;km/h.}$

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Additional Information:-

⠀⠀⠀⠀⠀✩ $\sf Speed = \dfrac{Distance}{Time}$

⠀⠀⠀⠀⠀✩ $\sf Velocity = \dfrac{Displacement}{Time}$

⠀⠀⠀⠀⠀✩ $\sf Acceleration = \dfrac{Final\; Velocity - Initial\; Velocity}{Time\;Taken}$

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★ Average:

• The mean is the average of the numbers. It is easily calculated by adding up all the numbers, then divide by how many numbers there are.

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