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:
141 comments Page 2 of 15.
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
Atul said:
1 decade ago
Question first line: man completes journey in 10 hrs.
In second line: he travels 1/2 of total distance (x) not the time at the rate of 21 km/hr
and 1/2 distance (x) not time at the rate of 25 km/hr.
TIME =DISTANCE/SPEED :1:((DISTANCE=1/2x)/(SPEED=21)for first half
:2:((DISTANCE=1/2x)/(SPEED=25)for second half
TOTAL TIME 10hrs =:1:+:2: =((1/2)x/21)+((1/2)x/24)
In second line: he travels 1/2 of total distance (x) not the time at the rate of 21 km/hr
and 1/2 distance (x) not time at the rate of 25 km/hr.
TIME =DISTANCE/SPEED :1:((DISTANCE=1/2x)/(SPEED=21)for first half
:2:((DISTANCE=1/2x)/(SPEED=25)for second half
TOTAL TIME 10hrs =:1:+:2: =((1/2)x/21)+((1/2)x/24)
Aleena said:
3 years ago
Let the time taken for the complete first half = x.
Then the time taken for complete second half will be = 10 - x.
Distance = speed * time.
So,
21x = 24(10-x)
21x = 240-24x
21x + 24x=240
45x = 240
x = 240/45
ie 16/3.
Give the value of x to the first equations.
21x=21 * 16/3.
We get 112.
24(10-x) = 24*(10-16/3).
We get 112.
Just add them both to get the total distance.
ie 224.
Then the time taken for complete second half will be = 10 - x.
Distance = speed * time.
So,
21x = 24(10-x)
21x = 240-24x
21x + 24x=240
45x = 240
x = 240/45
ie 16/3.
Give the value of x to the first equations.
21x=21 * 16/3.
We get 112.
24(10-x) = 24*(10-16/3).
We get 112.
Just add them both to get the total distance.
ie 224.
(7)
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.
Sri said:
1 decade ago
USE FORMULA :
Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,
The average speed during the whole journey is,
= 2(X)(Y)/(X)+(Y).
= 2(21)(24)/21+24.
= 1008/45.
= 22.4KM (AVERAGE SPEED).
NOW WE KNOW THE SPEED, SO SPEED = DISTANCE/TIME.
22.4 = DISTANCE/10 (MULTIPLYING 22.4 * 10 WE GET 224)
224 KMS.
Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,
The average speed during the whole journey is,
= 2(X)(Y)/(X)+(Y).
= 2(21)(24)/21+24.
= 1008/45.
= 22.4KM (AVERAGE SPEED).
NOW WE KNOW THE SPEED, SO SPEED = DISTANCE/TIME.
22.4 = DISTANCE/10 (MULTIPLYING 22.4 * 10 WE GET 224)
224 KMS.
Anshu said:
1 decade ago
Let the equal distance be x
[remember the value of x is the half the total distance]
speed are 21kmph and 24 kmph
we know that speed = distance time^-1
therefore,
time = distance speed^-1
10 = x/21 + x/24
10 = 24x + 21x / 504
5040 = 45x
560 = 5x
112 = x
since the x = 1/2 of the distance
total distance = 2x = 2 (112)= 224kmph
[remember the value of x is the half the total distance]
speed are 21kmph and 24 kmph
we know that speed = distance time^-1
therefore,
time = distance speed^-1
10 = x/21 + x/24
10 = 24x + 21x / 504
5040 = 45x
560 = 5x
112 = x
since the x = 1/2 of the distance
total distance = 2x = 2 (112)= 224kmph
Akshay said:
2 years ago
Total journey = 10hours.
Journey in 2 parts = 10/2 = 5.
Each journey is = 5hours.
1st journey speed = 21km/hr.
2nd journey speed = 24km/hr.
Total of 1st journey speed = 21 * 5 = 105
Total of 2nd journey speed = 24 * 5 = 120.
So,
Total 1st & 2nd both journey = 105 + 120.
= 225km.
Journey in 2 parts = 10/2 = 5.
Each journey is = 5hours.
1st journey speed = 21km/hr.
2nd journey speed = 24km/hr.
Total of 1st journey speed = 21 * 5 = 105
Total of 2nd journey speed = 24 * 5 = 120.
So,
Total 1st & 2nd both journey = 105 + 120.
= 225km.
(90)
Hardik H Bagaria said:
12 months ago
@All.
For the people who got an answer as 225km, we cannot assume that the time taken to complete half of the journey (distance) is 5hrs, assuming 5hrs for the first trip and 5 for the second is wrong.
Because its not relative to the time, but rather relative to the journey (distance).
For the people who got an answer as 225km, we cannot assume that the time taken to complete half of the journey (distance) is 5hrs, assuming 5hrs for the first trip and 5 for the second is wrong.
Because its not relative to the time, but rather relative to the journey (distance).
(48)
Hardik Maheshwari said:
5 years ago
I think the ans should be 225 because in first half mean in 5km he covered distance at a speed of 21kmph.
=21 * 5=105.
And in second half it mean 5km he covered distance at a speed of 24kmph =24 * 5=120.
By adding both distance=105 + 120 = 225.
Hence the ans should be 225.
=21 * 5=105.
And in second half it mean 5km he covered distance at a speed of 24kmph =24 * 5=120.
By adding both distance=105 + 120 = 225.
Hence the ans should be 225.
Surya said:
1 decade ago
To apply formula 2uv/(u+v),
Where,
s = Distance;
u = First Half velocity which is 21 kmph.
v = Second Half Velocity which is 24 kmph.
=> (2*21*24)/(21+24).
=> (1008)/45.
=>22.4 kmph.
Therefore, average speed = 22.4 km/hr.
s = vt.
s = 22.4 km/hr x 10hrs.
s = 224 km.
Where,
s = Distance;
u = First Half velocity which is 21 kmph.
v = Second Half Velocity which is 24 kmph.
=> (2*21*24)/(21+24).
=> (1008)/45.
=>22.4 kmph.
Therefore, average speed = 22.4 km/hr.
s = vt.
s = 22.4 km/hr x 10hrs.
s = 224 km.
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