Question

a car covers 1st half of distance with 40 km per hour and 2nd half with 60 km per hour then calculate average speed​

Answer 1

Given:

• Car covers 1st half distance with the speed of 40km/h
• And 2nd half distance with the speed of 60km/h

Find:

• Average speed of the car

Solution:

Let, total distance be s metre

So, Half Distance = s/2 metre

For f1st half distance

we, know that

$\boxed{\sf Time_{1} = \dfrac{Distance}{Speed}}$

where,

• Distance = s/2 m
• Speed = 40km/h

So,

$\dashrightarrow\sf Time_{1} = \dfrac{Distance}{Speed}$

$\dashrightarrow\sf Time_{1} = \dfrac{ \dfrac{s}{2} }{40}$

$\dashrightarrow\sf Time_{1} = \dfrac{s}{2} \times \dfrac{1}{40}$

$\dashrightarrow\sf Time_{1} = \dfrac{s}{80}$

$\therefore\sf Time \: for \: f1st \: half \: distance= \dfrac{s}{80}$

_________________________

Now, for 2nd Half Distance

Again, using

$\boxed{\sf Time_{2} = \dfrac{Distance}{Speed}}$

where,

• Distance = s/2 m
• Speed = 60km/h

So,

$\dashrightarrow\sf Time_{2} = \dfrac{Distance}{Speed}$

$\dashrightarrow\sf Time_{2} = \dfrac{ \dfrac{s}{2} }{60}$

$\dashrightarrow\sf Time_{2} = \dfrac{s}{2} \times \dfrac{1}{60}$

$\dashrightarrow\sf Time_{2} = \dfrac{s}{120}$

$\therefore\sf Time \: for \: 2nd \: half \: distance= \dfrac{s}{120}$

_________________________

Now, we know that

$\boxed{\sf Average \: Speed = \dfrac{Total \: Distance}{Total \: Time }}$

where,

• Total Distance = s/2 + s/2
• Total Time = s/80 + s/120

So,

$\dashrightarrow\sf Average \: Speed = \dfrac{Total \: Distance}{Total \: Time }$

$\dashrightarrow\sf Average \: Speed = \dfrac{ \dfrac{s}{2} + \dfrac{s}{2} }{ \dfrac{s}{80} + \dfrac{s}{120} }$

$\dashrightarrow\sf Average \: Speed = \dfrac{ \dfrac{s + s}{2} }{ \dfrac{3s + 2s}{240}}$

$\dashrightarrow\sf Average \: Speed = \dfrac{ \dfrac{2s}{2} }{ \dfrac{5s}{240}}$

$\dashrightarrow\sf Average \: Speed = \dfrac{2s}{2} \times \dfrac{240}{5s}$

$\dashrightarrow\sf Average \: Speed = s \times \dfrac{48}{s}$

$\dashrightarrow\sf Average \: Speed = \dfrac{48s}{s}$

$\dashrightarrow\sf Average \: Speed = 48km/h$

$\large{\therefore \pink{\sf Average \: Speed \: of \: the \: car \: will \: be \: 48km/h}}$