Question

a car covers a distance of 300 km with a speed of 60 km/h and then covers a distance of 450 km with a speed of 90 km/h.Calculate the average speed​

Answer 1

$\;\;{\textbf{\textsf{ AnswEr :-}}}$

$\small\boxed{\bf{\purple{Average \ speed = \ 75km/hr}}}$

___________________

$\;\;{\textbf{\textsf{ Given :-}}}$

◕ A car covers a distance of 300 km with a speed of 60 km/h and then covers a distance of 450 km with a speed of 90 km/h.

$\;\;{\textbf{\textsf{ To \ find :-}}}$

◕ Average speed

$\;\;{\textbf{\textsf{ Solution :-}}}$

As we know that,

$:\implies \bf{Speed = \dfrac{{Distance}}{{Time}}}$

$:\implies \bf{60 = \dfrac{{300}}{{Time}}}$

$:\implies \bf{Time = \dfrac{{300}}{{60}}}$

$:\implies \bf{ Time={{5 \: hrs}}}$

$:\implies \small\boxed{\bf{\pink{T1 = 5 hrs}}}$

$\sf \: Again \: ,$

$:\implies \bf{Speed = \dfrac{{Distance}}{{Time}}}$

$:\implies \bf{90 = \dfrac{{450}}{{Time}}}$

$:\implies \bf{Time = \dfrac{{450}}{{90}}}$

$:\implies \bf{ Time={{5 \: hrs}}}$

$:\implies \small\boxed{\bf{\pink{T2 = 5 hrs}}}$

__________________

$\bf{⇢ Average \: \: speed = \dfrac{{Average \: speed}}{{Total \: \: time \: taken}}}$

$\bf{⇢ Average \: \: speed =300 \: + \: \dfrac{{450}}{{5}}} \: + \: 5$

$\bf{⇢ Average \: \: speed \: \: = \dfrac{{750}}{{10}}}$

$:\implies \small\boxed{\bf{\purple{Average \: \: speed = 75km/hr}}}$

$\sf \: ∴ \: Hence, \: the \: average \: speed \: is \: 75km/hr.$

Answer 2

$\huge\bf{Answer :}$

Average speed of the car = 75 km/ h ✓

$\huge\bf{Concept :}$

• Here, we're asked to find the average speed of the car. Two situations are given according to which, we'll find the average speed.
• Firstly, we'll find the time taken by the car going through first situation and then find the time taken of car going from second situation.
• After finding both the time periods, we'll calculate the total average speed of the cars, because without both the time periods, we cannot find the average speed.
• We'll find the speed of the car from the relationship between distance, speed and time.

Let's solve the problem.

$\huge\bf{Given :}$

A) In the first situation :-

• Distance covered = 300 Km
• Speed of the car = 60 Km/h

B) In the second situation :-

• Distance covered = 450 Km
• Speed of the car = 90 Km/h

To find :

• Average speed of the car.

$\huge\bf{Explanation :}$

☆ In the first situation,

Distance ( d ) = 300 Km

Speed of the ( s ) = 60 Km/h

∴ We'll find the time taken from the formula of speed.

⇒ Speed = Distance / Time

⇒ 60 = 360 / Time

⇒ Time ( t ) = 5 Hours ------(i)

_____________________________

☆ In the second situation,

Distance ( d¹ ) = 450 Km

Speed of the car ( s¹ ) = 90 Km/h

⇒ Speed = Distance / Time

⇒ 90 = 450 / Time

⇒ Time ( t¹ ) = 5 hours --------(ii)

______________________________

Now, we'll find the average speed :-

Average speed = Total speed / Total time taken

⇒ 300+450 / 5 + 5

⇒ 750 / 10 = 75 Km / hour ✔️