Question

Abdul, while driving to school, compl e speed for his trip to be 20 km h-. On. his return trip along the 30 km h-!. What is the average speed for Abdul's trip?​

Answer 1

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${\large{\pmb{\sf{\bigstar \:{\underline{RequirEd \: Solution...}}}}}}$

$\: \: \: \: \: \:{\large{\pmb{\sf{\bigstar \:{\underline{By \: method \: first...}}}}}}$

ProvidEd that:

⋆ Average speed by going to a trip is equal to 20 kilometres per hour.

⋆ Average speed when returning from a trip is equal to 30 kilometres per hour.

To calculaTe:

⋆ Average speed for Abdul's trip

SolutioN:

⋆ Average speed for Abdul's trip = 24 kilometres per hour

Using concepts:

⋆ Dimension to calculate total distance

⋆ Average speed formula

⋆ Formula to calculate time taken

Using formulas:

• Total distance is given by,

• ${\small{\underline{\boxed{\sf{Total \: distance \: = 1st \: distance \: + 2nd \: distance}}}}}$

• Average speed is given by,

• ${\small{\underline{\boxed{\sf{v \: = \dfrac{s}{t}}}}}}$

Where, v denotes average speed, s denotes total distance and t denotes total time taken.

• Time is given by,

• ${\small{\underline{\boxed{\sf{t \: = \dfrac{s}{v}}}}}}$

Where, t denotes time taken, s denotes distance and v denotes speed

Assumption:

• Let the distance travelled by Abdul as a

Required solution:

~ Firstly finding total distance!

→ As he go to school and return back again from a distance,a therefore, the total distance becames

• Total distance = 2a

~ Now let us find out the time taken

$:\implies \sf Time \: taken \: = \dfrac{Distance}{Speed} \\ \\ :\implies \sf t \: = \dfrac{s}{v} \\ \\ :\implies \sf t \: = \dfrac{a}{20} + \dfrac{a}{30} \\ \\ \leadsto \sf Taking \: LCM \: of \: 20 \: and \: 30 \\ \\ :\implies \sf t \: = \dfrac{3 \times a + 2 \times a}{60} \\ \\ :\implies \sf t \: = \dfrac{3a + 2a}{60} \\ \\ :\implies \sf t \: = \dfrac{5a}{60} \\ \\ :\implies \sf Time \: = \dfrac{5a}{60} \: hour$

~ Now let us calculate the average speed!

$:\implies \sf Average \: speed \: = \dfrac{Total \: distance}{Total \: time} \\ \\ :\implies \sf v \: = \dfrac{s}{t} \\ \\ :\implies \sf v \: = \dfrac{\dfrac{2a}{5a}}{60} \\ \\ :\implies \sf v \: = \dfrac{2a \times 60}{5a} \\ \\ :\implies \sf v \: = \dfrac{2\not{a} \times 60}{5\not{a}} \\ \\ :\implies \sf v \: = \dfrac{2 \times 60}{5} \\ \\ :\implies \sf v \: = \dfrac{120}{5} \\ \\ :\implies \sf v \: = \cancel{\dfrac{120}{5}} \: (Cancelling) \\ \\ :\implies \sf v \: = 24 \: kmh^{-1}$

Therefore, average speed = 24 km/h

$\: \: \: \: \: \:{\large{\pmb{\sf{\bigstar \:{\underline{By \: method \: second...}}}}}}$

ProvidEd that:

⋆ Average speed by going to a trip is equal to 20 kilometres per hour.

⋆ Average speed when returning from a trip is equal to 30 kilometres per hour.

To calculaTe:

⋆ Average speed for Abdul's trip

SolutioN:

⋆ Average speed for Abdul's trip = 24 kilometres per hour

Using concept:

⋆ Average speed formula

Using formula:

• ${\small{\underline{\boxed{\sf{v \: = \dfrac{2 \: v_1 \: v_2}{v_1 \: + v_2}}}}}}$

Where, v denotes average speed, v_1 denotes speed first and v_2 denotes speed second.

Required solution:

$:\implies \sf v \: = \dfrac{2 \: v_1 \: v_2}{v_1 \: + v_2} \\ \\ :\implies \sf v \: = \dfrac{2 \times 20 \times 30}{20 + 30} \\ \\ :\implies \sf v \: = \dfrac{2 \times 600}{50} \\ \\ :\implies \sf v \: = \dfrac{1200}{50} \\ \\ :\implies \sf v \: = \cancel{\dfrac{1200}{50}} \: (Cancelling) \\ \\ :\implies \sf v \: = 24 \: kmh^{-1}$

Average speed = 24 km/h

Answer 2

Given that

Abdul, while driving to school, compl e speed for his trip to be 20 km h-. On. his return trip along the 30 km h-!. What is the average speed for Abdul's trip?

We need to find

The average speed for Abdul’s trip

Solution

Let us take the following assumptions for calculating the average speed for Abdul’s trip

As per the given data in the question

Average speed from home to school v1av = 20km h-1

Average speed from School to Home v2av = 30km h-1

Our assumptions

The distance Abdul commutes while driving from Home to School = S

Let us assume the time taken by Abdul to commutes this distance = t1

Distance Abdul commutes while driving from School to Home = S

Let us assume the time taken by Abdul to commutes this distance = t2

Also, we know that

The time is taken from Home to School t1=S/v1av

Similarly, Time is taken from School to Home t2=S/v2av

Total distance

Total distance from home to school and backward = 2S——-(i)

Total time is taken from home to school and backward (T)=S/20+S/30———-(ii)

Formula

Speed = Distance / Time

Therefore,

Average Speed(Vav)for covering total distance (2s)=Total Distance/Total Time

So from equations (i) and (ii) we get,

Average Speed(Vav) =2S/(S/20+S/30)

=2S/[30S+20S)/600] =1200S/50S

=24kmh-1

Final Answer

The average speed for Abdul’s trip = 24kmh-1