Aptitude - Time and Distance - Discussion
Discussion Forum : Time and Distance - General Questions (Q.No. 7)
7.
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Answer: Option
Explanation:
| (1/2)x | + | (1/2)x | = 10 |
| 21 | 24 |
 |
x | + | x | = 20 |
| 21 | 24 |
15x = 168 x 20
| x = |
 |
168 x 20 |  |
= 224 km. |
| 15 |
Discussion:
143 comments Page 7 of 15.
Ramana said:
1 decade ago
We know that when dist traveled is equal the its harmonic mean so,
we can get by => avg speed*time= dist.
= 2(21*24)/21+24.
= 1008/45 = 22.4KM/hr.
Avg speed = 22.4km/hr.
Distance = Speed* time = 22.4*10 = 224 km.
we can get by => avg speed*time= dist.
= 2(21*24)/21+24.
= 1008/45 = 22.4KM/hr.
Avg speed = 22.4km/hr.
Distance = Speed* time = 22.4*10 = 224 km.
K Padmanaban said:
1 decade ago
The derived answer is as far as I am concerned is wrong. Because it is clearly stated that half of the journey is @21 kmph and rest is @24 kmph.
We can simply take the average speed as (21+24)/2 = 45/2.
And multiply the speed with the time taken i.e 45/2*10 = 225 km.
It is simple to derive from the distance formula i.e.
Distance = speed * time taken
Got it.
We can simply take the average speed as (21+24)/2 = 45/2.
And multiply the speed with the time taken i.e 45/2*10 = 225 km.
It is simple to derive from the distance formula i.e.
Distance = speed * time taken
Got it.
Jing said:
1 decade ago
@Muhammed way is incorrect because, you can't just assume that first half equals second half equals 5 hours. Your speed is different in the two halves of the journey. You are going slower at first half but faster at second half. So you are taking a bit more than 5 hours in first half, and a bit less than 5 hours in second half. We have to weight that first. 224 km is the correct answer, 225 km is not.
Sid said:
1 decade ago
@Mohammed is wrong.
Because,
Average speed is the weighted average with the time traveled at the different speeds being the weight & not the distance traveled at different speeds.
Because,
Average speed is the weighted average with the time traveled at the different speeds being the weight & not the distance traveled at different speeds.
Sid said:
1 decade ago
Hey guys. There's a easy way to solve this.
When distance is equal in both halves then use this formula,
2*u*v/u+v(where u and v are the given speeds pertaining to given distances).
Here u is 21 and v is 24.
So according to our formula we have,
2*21*24/21+24=1008/45=112/5=22.4.
So now according to TSD formula,
Speed = distance /time.
Hence 22.4 = d/10.
Thus d = 22.4*10 = 224kms
When distance is equal in both halves then use this formula,
2*u*v/u+v(where u and v are the given speeds pertaining to given distances).
Here u is 21 and v is 24.
So according to our formula we have,
2*21*24/21+24=1008/45=112/5=22.4.
So now according to TSD formula,
Speed = distance /time.
Hence 22.4 = d/10.
Thus d = 22.4*10 = 224kms
S.vikash said:
1 decade ago
How you multiplied with (1/2) in first step?
Manhar said:
1 decade ago
Hi @Vikash.
Let the total distance = X (becoz we don't know the total distance or journey).
So, 1st half means X/2, 2nd half means also X/2.
That's why we can multiplied with(1/2) in first step.
Let the total distance = X (becoz we don't know the total distance or journey).
So, 1st half means X/2, 2nd half means also X/2.
That's why we can multiplied with(1/2) in first step.
Vissu said:
1 decade ago
Its simple. Average of two speeds 21 kmphr and 24 kmphr is 1008/45.
Now dist = speed x time = (1008/45) x 10 = 224.
Now dist = speed x time = (1008/45) x 10 = 224.
Leelakrishna said:
1 decade ago
2/v = (1/v1)+(1/v2) find v then d = v*t.
Chandan pal said:
1 decade ago
Avg speed: 2xy/x+y.
Avg speed: 2*21*24/21+24 = 112/5.
Distance = (112/5)*10 = 224.
Avg speed: 2*21*24/21+24 = 112/5.
Distance = (112/5)*10 = 224.
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