A man travels equal distances of his journey at 40, 30 and 15 km/h. respectively. Find his average speed for whole journey.
A. 24
B. 25
C. 27
D. 28
Answer: Option A
Solution(By Examveda Team)
Required average speed,$$ = {\frac{{\left( {3 \times 40 \times 30 \times 15} \right)}}{{ {\left( {40 \times 30} \right) + \left( {40 \times 15} \right) + \left( {30 \times 15} \right)} }}} $$
$$ = 24\,{\text{km/hr}}$$
Alternatively
Time taken to traveled $$\frac{1}{3}$$ distance of journey with speed 40 kmph,
$$ = \frac{{ {\frac{1}{3}} }}{{40}} = \frac{1}{{120}}$$
Time taken to traveled $$\frac{1}{3}$$ distance of journey with speed 30 kmph,
$$ = \frac{{ {\frac{1}{3}} }}{{30}} = \frac{1}{{90}}$$
Time taken to traveled $$\frac{1}{3}$$ distance of journey with speed 15 kmph,
$$\eqalign{ & = \frac{{ {\frac{1}{3}} }}{{15}} = \frac{1}{{45}} \cr & {\text{Total time taken}} \cr & = {\frac{1}{{120}}} + {\frac{1}{{90}}} + {\frac{1}{{45}}} \cr & = \frac{{45}}{{1080}} \cr & {\text{Average speed}} \cr & = \frac{{{\text{Total distance traveled}}}}{{{\text{Total time taken}}}} \cr & = \frac{1}{{ {\frac{{45}}{{1080}}} }} \cr & = 24\,{\text{kmph}} \cr} $$
Join The Discussion
Comments ( 7 )
Related Questions on Average
A. 125 km/hr
B. 75 km/hr
C. 135 km/hr
D. 120 km/hr
24 it is a wrong answer and 27 is the correct answer
Let, Distance of one person 120(LCM of 40,30,15)
1st Journy time taken by=120/40=3
2nd.................................. =120/30=4
3rd!.................................=120/15=8
Average Speed=Total distance/Total Time
=360/15=24
Thanks
avg distance formula= 3÷(1/x+1/y+1/z)
now we have 1/40+1/30+1/15
Lcm of 40,30,15 is 120
then (3+4+8)/120=1/8
from above formula 3÷1/8=3×8
so ans=24
Let ,Distance=x
Since three separate speed completed the distance.
So one part is x/3
Now ,45km go by 1h
1 " " " " "=1/45
X/3 " =x×1/45×3=x/120
At the same way....x/90,x/45.
Total time taken=x/120+x/90+x/45=15x/360=x/24.
So,average speed=Distance/Time=x/x/24=24.
Time taken to traveled 1/3 distance of journey with speed 40 kmph,
= (1/3)/40 = 1/120.
Time taken to traveled 1/3 distance of journey with speed 30 kmph,
= (1/3)/30 = 1/90.
Time taken to traveled 1/3 distance of journey with speed 15 kmph,
= (1/3)/15 = 1/45.
Total time Taken = (1/120) + (1/90) + (1/45) = 45/1080.
Average speed = Total distance traveled /total time taken = 1/(45/1080) = 24 kmph.
i did not understand this question please give me the brief explaination
but what is the formula used