Question

5. If a person travels two equal distances at 20kmph
and 30kmph respectively, what is his average speed?
A) 24
B) 25
C) 22
D) 23​

Answer 1

Answer:-

Let ,

The distance travelled be d km.

Given:-

The person travelled d km with a speed of 20 km/h.

We know,

Time = Distance/speed

So,

⟹ Time taken to travel d km = (d/20) hrs

Also given that,

The person again travels the same distance i.e., d km with a speed of 30 km/h.

⟹ Time taken to travel d km = (d/30) hrs

We know that,

Average speed = Total distance travelled/Total time taken.

⟹ Average speed of the person = (d + d) / (d/20 + d/30)

⟹ Average speed of the person = 2d × 60/ (3d + 2)d

⟹ Average speed of the person = 120d/5d

⟹ Average speed of the person = 24 km/hr

Answer 2

$\Large{\bf{Given\::}}$

• A person travels two equal distance at 20 km/h & 30 km/h respectively.

$\\ \Large{\bf{To\: Find\::}}$

• Average speed of the person.

$\\ \Large{\bf{Solution\::}}$

Let,

• That person travels x km.

Then,

➣ It is given that, the person travels 2 times the same distance, i.e. x km.

$:\implies\:\tt{Total\: distance\:=\:(x\:+\:x)\:km\:}$

$:\implies\:\bf{Total\: distance\:=\:(2x)\:km\:}$

Now,

It is given that,

➣ In first time of his travel he moves at 20 km/h.

As we know that,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Speed\:=\:\dfrac{Distance}{Time}\:}\:{\Large\mid}\:\green\bigstar$

$:\implies\:\tt{20\:=\:\dfrac{x}{(Time)_1}\:}$

$:\implies\:\tt{(Time)_1\:=\:\left(\dfrac{x}{20}\right)\: hours}$

And,

➣ In second time of his travel he moves at 30 km/h.

$:\implies\:\tt{30\:=\:\dfrac{x}{(Time)_2}\:}$

$:\implies\:\tt{(Time)_2\:=\:\left(\dfrac{x}{30}\right)\: hours}$

As we know that,

$\orange\bigstar\:{\Large\mid}\:\bf\blue{Avg.\:speed\:=\:\dfrac{Total\:distance}{Total\:time}\:}\:{\Large\mid}\:\green\bigstar$

$:\implies\:\tt{Avg.\:Speed\:=\:\dfrac{2x}{(Time)_1\:+\:(Time)_2}\:}$

$:\implies\:\tt{Avg.\:Speed\:=\:\dfrac{2x}{\frac{x}{20}\:+\:\frac{x}{30}}\:}$

$:\implies\:\tt{Avg.\:Speed\:=\:\dfrac{2x}{\frac{3x\:+\:2x}{60}}\:}$

$:\implies\:\tt{Avg.\:Speed\:=\:\dfrac{2x}{\frac{5x}{60}}\:}$

$:\implies\:\tt{Avg.\:Speed\:=\:2x\times{\dfrac{60}{5x}}\:}$

$:\implies\:\tt{Avg.\:Speed\:=\:2\times{\dfrac{60}{5}}\:}$

$:\implies\:\tt{Avg.\:Speed\:=\:2\times{12}\:}$

$:\implies\:\bf\pink{Avg.\:Speed\:=\:24\:km/h\:}$