Question

3. Abdul, while driving to school, computes the average speed for
his trip to be 20 km hl. On his return trip along the same
route, there is less traffic and the average speed is
30 km h-!. What is the average speed for Abdul's trip?
​

Answer 1

Answer:

24kmph( or 24 kmh^-1{inverse})

Explanation:

Given , his speeds are 20kmph and 30kmph

We need to find the average speed.

So ,

Let the total distance Be ‘x’ km

From basic formula ,

Distance = speed x time

Case 1:

For 20 kms

x = V1 x t1 = 20(t1)

Case 2:

For 30km

=> x =V2 x t2 = 30(t2)

Average speed = total distance travelled / total time taken

=> V’= x + x /x/v1+ x/v2 = 2x/x/20+x/30

=> V’ = 24 kmph

(Refer attachment)!

Answer 2

Question:

$\:$

• Abdul, while driving to school computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 30 km/h. What is the average speed for Abdul's trip?

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Answer:

$\:$

• Average speed for Abdul's trip is 24 km/h.

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ㅤㅤㅤStep - By - Step Explanation

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★ Given that . . .

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• Average speed while he was driving to school = 20 km/h

• Average speed when he returns = 30 km/h

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★ To Find . . .

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• Average speed for Abdul's trip?

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★ Required Solution . . .

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Let,

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• Distance while going to school = distance when he returns = x km

• Speed while he goes to school be $\pmb{\bf{v_{1}}}$

• Speed when he returns be $\pmb{\bf{v_{2}}}$

• Time taken to reach school be $\pmb{\bf{t_{1}}}$

• Time taken when he returns be $\pmb{\bf{t_{2}}}$

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We know that,

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$\bigstar\:\boxed{\pmb{\bf{\pink{Distance = Speed\:\times\:Time}}}}$

$\:$

$\underline{\pmb{\bm{\bigstar\:Putting\:all\:values\:. \:. \:.}}}$

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• In first case

$\\ \qquad\qquad\leadsto\:\sf x = v_{1}\:\times\:t_{1} \\ \\ \qquad\qquad\leadsto\:\sf x = 20\:\times\:t_{1} \\ \\ \qquad\qquad\leadsto\:\underline{\boxed{\pmb{\bf{\purple{t_{1} = \dfrac{x}{20}}}}}}\:\bigstar$

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• In second case

$\\ \qquad\qquad\leadsto\:\sf x = v_{2}\:\times\:t_{2} \\ \\ \qquad\qquad\leadsto\:\sf x = 30\:\times\:t_{2} \\ \\ \qquad\qquad\leadsto\:\underline{\boxed{\pmb{\bf{\green{t_{2} = \dfrac{x}{30}}}}}}\:\bigstar$

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• Now, using formula of average speed ::

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$\bigstar\:\boxed{\pmb{\bf{\blue{Average\:speed = \dfrac{Total\:distance\:travelled}{Total\:time\:taken}}}}}$

$\:$

$\underline{\pmb{\bm{\bigstar\:Putting\:all\:values\:. \:. \:.}}}$

$\\ :\implies\:\sf Average\:speed = \dfrac{x + x}{t_{1} + t_{2}} \\ \\ :\implies\:\sf Average\:speed = \dfrac{2x}{\dfrac{x}{20} + \dfrac{x}{30}} \\ \\ :\implies\:\sf Average\:speed = \dfrac{2x}{\dfrac{3x + 2x}{60}} \\ \\ :\implies\:\sf Average\:speed = \dfrac{2x}{\dfrac{5x}{60}} \\ \\ :\implies\:\sf Average\:speed = 2x\:\div\:\dfrac{5x}{60} \\ \\ :\implies\:\sf Average\:speed = 2x\:\times\:\dfrac{60}{5x} \\ \\ :\implies\:\sf Average\:speed = 2\:\times\:\cancel{x}\:\times\:\dfrac{60}{5\:\times\:\cancel{x}} \\ \\ :\implies\:\sf Average\:speed = 2\:\times\:{\cancel{\dfrac{60}{5}}} \\ \\ :\implies\:\sf Average\:speed = 2\:\times\:12 \\ \\ :\implies\:\underline{\boxed{\pmb{\bf{\red{Average\:speed = 24\:km/h}}}}}\:\bigstar$

$\\ \therefore\:{\underline{\sf{Hence,\:average\:speed\:for\:Abdul's\:trip\:is\:\pmb{\orange{24\:km/h}}}}}$

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