Aptitude - Time and Distance - Discussion

The persons speed of walking is 14km/hr.
He should have walked 10km/hr.
If he had gone with the speed of 10km/hr then he would have walked more den 20km/hr.
So,We are supposed to imagine if he had walked 10km/hr speed then what would be his actual speed.
So,we assume that let the distance be X km.


Then, the formula comes into picture i.e. speed=distance/time

So , as we are supposed to find as per the expectation if he had walked 10km/hr :
we take 10km/hr as his walking speed.
Distance is we are supposed to find more than 20
i.e. 20+X.
time is what the person actually doing .In reality the person is walking at 14km/hr.

So,in short with respect to person's capacity i.e. 14km/hr we can find the exact answer.
and therefore

Another formula for 10km/hr is :
time =distance by speed
i.e. time=X/10

time= X / 10 becomes the 1st equation....
time= (X + 20 ) / 14 becomes second equation....
from the above 2 eqns :
(X / 10 ) = (( X + 20 ) / 14)
then solve the further equation ....
Hope u got it :)

Let distance travelled by person at 14km/h be d1 and distance travelled at 10km/h be d2.

d1-d2=20km (given in Q that he walks 20km more)
D=speed * time.

{Time is constant and reason is;

It is because supposed for example if a person walks 10km/h for 7 hrs means he would have covered 70km. If speed changes to 14km/h and if we assume time is not constant then to cover 70km distance at 14km/h 5hrs would be needed, then in such case there would be no case of extra distance covered like in present Q which is 20km.

If time is constant like 7hrs so at distance at 10km/h =70km & 14km/h=98km and only then we can say it travelled 28km extra)}

Now coming to the present Q,
d1-d2=20km,
14t-10t=20.
t(14-10)=20.
4t=20.
T=5hr.

Q says if a person walks 14km/h that means 14km/h is not the original speed...
D=10*5=50km.

Most people have the confusion that time is equal has not been stated equal in the question, Then, how can we equate the two entities based on the assuption that time is equal, right?


Let me explain;
if t=1st hour, distance=10...also, distance=14
t=2nd hour, distance=20...also distance=14+14=28
..
.
Similarly when t=5th hour, distance=50...distance=70
Now, the difference in respective distances =70-50=20
This means that the distance covered is 20 more in the 5th hour when speed is 14kmph instead of 10kmph.
This means, in the same time, the distance covered is different(i.e. 20km more->as stated in the question)
This proves that the time interval is the same irrespective of speed is different.
So, we equated the two statements since the time taken has to be the same. Hope you got it.

Detailed Explanation:

Cconsider,
Z is actual distance travelled (when going at 10km/hr).
X is time (Unknown).

Case: 1
travelling at normal speed (10Km/hr).
10Km-----------------@1 hr
ZKm-------------------@X hr

after cross multiplying each other we get;
10X=Z*1 means that 10X=Z---------1)

Case 2:
Travelling at 14Km/hr.
|||y
14Km-------------@1hr.
20+ZKm----------@Xhr.

here, 20+Z means 20Km + Z Km travelled by Normal Speed @ same X hour.

by cross multiplying we get,
14X=20+Z-----------------2)

just solve both equation 1) & 2.
sub 1 in 2
Z=10X ,we get 14X=20+10X.
so, 4X=20 , X=5 now, we are not questioned for hours but only we need distance so,sub X directly in equation 2).

We get 70=20+Z so Z = 70-20 = 50Km.

See if the person generally walk at the speed of 10 km/hr but he walk 14 km/hr and by this speed he walk 20 km more. Means from this extra 4 km speed he covers the extra distance of extra 20 km in 5 hours.

So if he walk 5 hour at the speed of 10 km/hr the distance cover is 50 km and with the speed of 14 km/hr he covers 70 km. But he is a man and he has its stamina also means more speed less time of walking because he tired at the same point of his body capacity in both speed.

So if he will a machine then the answer is 70 km but he is a man and hence we have to deduce the extra 20 km and the answer is 50 km.

So much complicated answers who said time is not given.

The man travels with different speeds but for the same time.

Let's assume that time as x.

Now for the same time, the distance travelled is different because speed is different.

Now Distance = Speed*Time.

For the same time, distance travelled will be greater for higher speed i.e. 14 kmph and the difference of distance is 20 km.

So 14x-10x = 20 (since 20 km more). x = 5 i.e. Time = 5 hrs.

So actual distance is 10*x = 10*5 = 50 kmph.

The answer comes in two steps I explained to make it easier.

Here time is never given.

So consider man named.

Ashok walk with speed 10 km/hr, he travel for next 2 hour so distance he cover is 20 km.

2nd person named.

Madhu walk with speed 14 km/hr, he also travel for 2 hour so distance he cover is 28 km.

Now Madhu travel more 20 km wit speed 14 km/hr. So we subtract that 20 km from distance he travel in 2 hour.

= 28-20 = 8 km.

It means if we consider time 2 hour. Which is not given, so the answer will be 8 km?

Is it true?

Time = Distance / Speed
Let Distance = x
First Case : Person's usual speed is 10km/hr
So, T = D/S and putting the values in formula we get : T = x/10

Second case : if he travels at the speed of 14km/hr then he would have walked 20 km more.

We have already assumed distance as x and now in second case we have 20 km more So:
T=D/S, x+20/14

So, we have:
x/10 = x+20/14
And solving the above ,we get
14x = 10x+200
14x - 10x = 200
4x = 200
x = 50Km

@All.

According to me;

1st hour 10 = 14,
2nd hour 20 = 28,
3rd hour 30 = 42,
4th hour 40 = 56,
5th hour 50 = 70,

IF IN ONE HOUR HE IS DOING 14, THEN IN THE FIFTH HOUR (14*5=60) TIMES UP.

At speed 10 kmph he reaches 50 km at the same time if he travels in 14 kmph he would reach 70 km.

So, 70 - 50 = 20. I think u got it.

OR
14-10 = 4km/hr.
4km/hr = 20km travelled.
so 1hr = 5km,
then 10km/hr = 10 * 5 = 50.

Note: That in both speed Time will be same so

for speed 10km/hr speed=distance/time
10 =x/time1
for speed 14km/hr 14 =(x+20)/time2

: Note time will be same so we equate these two equations respect with time

time1 = time2
time1 = x/10
time2 = (x+20)/14
(X/10)=(X+20)/14
we solve this to obation right answer