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.
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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.
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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!?
Average speed = 36 kmph!
★ According to method 1st!
→ Let the distance = a
→ Therefore, the total distance = 2a
~ As we already know that
And here, in this question we have to use this formula too!
~ Finding time in case first!
[tex]:\implies \sf Time \: = \dfrac{Distance}{Speed} \\ \\ :\implies \sf Time \: = \dfrac{a}{30} \\ \\ {\pmb{\sf{Henceforth, \: done!}}}[/tex]
~ Now finding time in case second!
[tex]:\implies \sf Time \: = \dfrac{Distance}{Speed} \\ \\ :\implies \sf Time \: = \dfrac{a}{45} \\ \\ {\pmb{\sf{Henceforth, \: done!}}}[/tex]
~ Now let's find out the total time!
[tex]:\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!}}}[/tex]
~ Now let's find out the average speed by using the below mentioned formula!
[tex]:\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!}}}[/tex]
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★ According to method 2nd!
~ Let's find out the average speed by using the below mentioned formula!
Where, v denotes average speed, v_1 denotes speed first and v_2 denotes speed second!
[tex]:\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!}}}[/tex]
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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