Question

2. A car travels the first half of a distance
between two places a speed of 30 km/hr
and the second half of the distance a
50 km/hr. The average speed of the car for
the whole journey is​

Answer 1

Answer:

$\large{\underline{\boxed{\sf Average \: Speed = 37.5 \: km/hr}}}$

Explanation:

Let the total distance of the journey be 2x km.

For half of the distance, i.e., x km -

• Distance = x km
• Speed = 30 km/h

Time = $\rm \dfrac{Distance}{Speed}$

⇒ Time₁ = $\rm \dfrac{x}{30} \: hrs$

$\rule{300}{2}$

For the next half distance, i.e., x km -

• Distance = x km
• Speed = 50 km/h

Time = $\rm \dfrac{Distance}{Speed}$

⇒ Time₂ = $\rm \dfrac{x}{50} \: hrs$

So, we need the total time taken.

⇒ Total time = $\rm \dfrac{x}{30} + \dfrac{x}{50}$

⇒ Total time = $\rm \dfrac{5x + 3x}{150}$

⇒ Total time = $\rm \dfrac{8x}{150}$

Now, we know that ;

$\rm Average \: Speed = \dfrac{Total \: Distance}{Total \: time \: taken}$

$\rm Average \: Speed = \frac{2x}{ \frac{8x}{150} } \\ \\ \rm Average \: Speed =2x \times \frac{150}{8x} \\ \\ \rm Average \: Speed = \frac{75}{2} \\ \\ \rm Average \: Speed =37.5 \: km/hr$

Hence, the average speed of the car is 37.5 km/hrs.

Answer 2

Answer:

Average speed of the car = 37.5 km/h

Step by step explanations :

given that,

A car travels the first half of a distance

between two places a speed of 30 km/hr

and the second half of the distance a

50 km/h

let the total distance travelled by the car be d

so,

time taken

to cover d/2 distance at a speed of

30 km/h = (d/2)/30

= d/60 h

also,

time taken to cover d/2 distance at a speed of 50 km/h = (d/2)/50

= d/100

Average speed

= total distance travelled/total time taken

here,

total distance travelled = d

and,

total time taken

= d/60 + d/100

(5d + 3d)/300

= 8d/300

= 2d/75

so,

total time taken = 2d/75

now,

Average speed =

total distance travelled/total time taken

putting the values,

Average speed = d/(2d/75)

= 75d/2d

= 75/2

= 37.5 km/h

so,

The average speed of the car for the whole journey =

37.5 km/h