Question

A car travels at a speed of 80 km/h during the first half of its running time and at
40 km/h during the other half. Find the average speed of the car.
​

Answer 1

Answer:

The average speed of the car is 60 km/h.

Answer 2

Required Answer:

Given:

• Speed of the car during 1st half = 80km/h

• Speed of the car during other half = 40km/h

To calculate:

• Average speed of the car

Calculation:

We know that,

• ${\underline {\boxed {\small {\bf \gray { Average \: Speed = \dfrac{Total \: distance}{Total \: time} } }}}}$

Calculating total distance covered:

Let us assume the car travelled by the speed in each half in " t " time.

→ Distance covered in first half:

Distance $\sf { (d_1) }$ = Speed × time

Distance $\sf { (d_1 )}$ = 80 × t

Distance $\sf { (d_1 )}$ = 80t

→ Distance covered in another half:

Distance $\sf { (d_2 )}$ = Speed × time

Distance $\sf { (d_2 )}$ = 40 × t

Distance $\sf { (d_2 )}$ = 40t

$\therefore$ Total distance = Distance covered in first half + Distance covered in another half

$\longmapsto$ Total distance = 80t + 40t

$\longmapsto$ Total distance = 120t

_______________________

Calculating total time:

As we assumed that “ the car travelled by the speed in each half in " t " time”.

$\therefore$ Total time = t + t

$\longmapsto$ Total time = 2t

_______________________

Now, substitute the value of "total distance travelled" and "total time taken" in the formula of average speed:

• ${\underline {\boxed {\small {\sf \pink { Average \: Speed = \dfrac{Total \: distance}{Total \: time} } }}}}$

$\sf { \longmapsto Average \: Speed = \dfrac{120t}{2t} }$

$\longmapsto$ ${\underline {\boxed {\large {\mathfrak \purple { Average \: Speed = 60 \: km/h } }}}}$

$\underline{\sf { \therefore Average \: speed \: is \: \textsf{\textbf{60 \: km/h }}}}$

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