Question

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

Answer 1

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 at a speed of 30 km/hr

and the second half of the distance at 50 km/hr.

1st Method :

let the total distance travelled by car

be s

so,

time taken to cover s/2 at 30 km/h

= (s/2)/30

= s/60 h

time taken to cover s/2 at 50 km/h

= (s/2)/50

= s/100 h

now,

Average speed of the car = total distance covered/total time taken

total distance covered = s

total time taken = s/60 + s/100

(5s + 3s) /300

8s/300

= 2s/75 h

so,

now we have,

distance covered = s

time taken = 2s/75

so,

Average speed = s/(2s/75)

= 75s/2s

= 75/2 km/h

= 37.5 km/h

so,

Average speed of the bus

= 37.5 km/h

________________

2nd Method :

let the 1st speed be V1

2nd speed be V2

so,

V1 = 30 km/h

V2 = 50 km/h

Average speed

= 2V1V2/(V1 + V2)

putting the values,

2 × 30 × 50/(30 + 50)

60 × 50/80

75/2

37.5 km /h

so,

Average speed of car = 37.5 km/h

Answer 2

$\bold {\huge {Your ~answer :-}}$

$\bf\huge\boxed{37.5\:km/h}$

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Explanation —

Given-

v1 = 30 km/h

v2 = 50 km/h

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We know that

Average speed<v>

$\huge v = \frac{distance}{total\:time}$

Now,

Let s be the total distance

So,

$= > v = \frac{s}{t}$

Simce t can be written as

s = vt => t = s/v

$= > v = \frac{s}{ \frac{s1}{v1} + \frac{s2}{v2} }$

Now putting

Since half of the distance therefore we can write s------> s/2

$= > v = \frac{s}{ \frac{ \frac{s}{2} }{30} + \frac{ \frac{s}{2} }{50} }$

On solving we got

=> v = 37.5

Therefore average speed of the car is 37.5 km/h

$\huge{\red{\ddot{\smile}}}$