Question

A motorcyclist drives from A to B with a uniform speed of 30 km/h and returns back with a speed of 45 km/h. Find its average speed.​

Answer 1

Answer:

Provided that:

A motorcyclist drives from A to B with a uniform speed of 30 kmph and returns back with a speed of 45 kmph. Find its average speed!?

• Going speed = 30 kmph
• Returning speed = 45 kmph
• Average speed = ???

Average speed = 36 kmph!

★ According to method 1st!

→ Let the distance = a

→ Therefore, the total distance = 2a

~ As we already know that

• ${\small{\underline{\boxed{\pmb{\sf{Time \: = \dfrac{Distance}{Speed}}}}}}}$

And here, in this question we have to use this formula too!

~ Finding time in case first!

$:\implies \sf Time \: = \dfrac{Distance}{Speed} \\ \\ :\implies \sf Time \: = \dfrac{a}{30} \\ \\ {\pmb{\sf{Henceforth, \: done!}}}$

~ Now finding time in case second!

$:\implies \sf Time \: = \dfrac{Distance}{Speed} \\ \\ :\implies \sf Time \: = \dfrac{a}{45} \\ \\ {\pmb{\sf{Henceforth, \: done!}}}$

~ Now let's find out the total time!

$:\implies \sf Total \: time \: = \dfrac{a}{30} + \dfrac{a}{45} \\ \\ \sf \leadsto By \: taking \: LCM \: we \: get \\ \\ :\implies \sf Total \: time \: = \dfrac{3 \times a + 2 \times a}{90} \\ \\ :\implies \sf Total \: time \: = \dfrac{3a + 2a}{90} \\ \\ :\implies \sf Total \: time \: = \dfrac{5a}{90} \\ \\ {\pmb{\sf{Henceforth, \: done!}}}$

~ Now let's find out the average speed by using the below mentioned formula!

• ${\small{\underline{\boxed{\pmb{\sf{Average \: speed \: = \dfrac{Total \: distance}{Time}}}}}}}$

$:\implies \sf Average \: speed \: = \dfrac{Total \: distance}{Time} \\ \\ :\implies \sf Average \: speed \: = \dfrac{\dfrac{2a}{5a}}{90} \\ \\ :\implies \sf Average \: speed \: = \dfrac{2a \times 90}{5a} \\ \\ :\implies \sf Average \: speed \: = \dfrac{2\not{a} \times 90}{5\not{a}} \\ \\ :\implies \sf Average \: speed \: = \dfrac{2 \times 90}{5} \\ \\ :\implies \sf Average \: speed \: = \dfrac{180}{5} \\ \\ :\implies \sf Average \: speed \: = 36 \: kmph \\ \\ {\pmb{\sf{Henceforth, \: solved!}}}$

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★ According to method 2nd!

~ Let's find out the average speed by using the below mentioned formula!

• ${\small{\underline{\boxed{\pmb{\sf{v \: = \dfrac{2v_1v_2}{v_1 + v_2}}}}}}}$

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

$:\implies \sf v \: = \dfrac{2v_1v_1}{v_1 + v_2} \\ \\ :\implies \sf v \: = \dfrac{2 \times 30 \times 45}{30 + 45} \\ \\ :\implies \sf v \: = \dfrac{60 \times 45}{75} \\ \\ :\implies \sf v \: = \dfrac{2700}{75} \\ \\ :\implies \sf v \: = 36 \: kmph \\ \\ :\implies \sf Average \: speed \: = 36 \: kmph \\ \\ {\pmb{\sf{Henceforth, \: solved!}}}$

Note:

→ The second formula is applicable only if distance is equal!

→ Please don't use the second method if you aren't in class 11th or more + because this formula will start from class 11th so if you want to apply this and you aren't in class 11th or more + then kindly ask your teacher that will you use it or not, you will get marking or not, are you accepting it? Please then use it.

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