Aptitude - Time and Distance - Discussion

@All.

My explanation is very simple;
T = D/S.

Suppose the speed of Abhay is x.

First case:
It takes 2 hours more than Samir.
T + 2 = 30/x ---> (1)

Second case:
when speed is double then 2x
it takes 1 hour less so
T-1=30/2x ----> (2)

Compare eq 1 &2;
30/x-2=T.
30/2x+1=T.

30/x-30/2x = 3.

Solving the above eq we get x=5km/h=> Abhay's speed.

Let the speed of Sameer be x.
Then, Ajay's speed = x+2.
When Ajay doubles his speed,
2(x+2) = x -1
or,2x+4 = x-1
Since speed can never be negative.
x=5.

Take the ratio of the speed of Abhay:
1:2

Then the inverse time we get Time ratio,
So:
2:1.

The Gap is 1 unit and this one is given as the sum of hours which is 3 hours.

So 2=6 hours and 1= 3 hours.

So we get the ans by applying a formula that is S= D/T
S= 30/6, which is equal to 5.

t+2 = 30/s ----> 1
t-1 = 30/2s ---- > 2

Solving this equation, we get;
s = 5.

Let Abhay's speed=x, Sameer's time=y
Case 1: 30/x = 2+y.
Case 2: 30/2x = y-1.
30/x-30/2x = (2+y)-(y-1),
= 2+y-y+1,
= 3.
We get the equation:
30/x-30/2x = 3.

By solving we will get the answer.

@Arun Kumar

Use 2 variables x and y, then it will be super easy.
Speed = distance/time.
Time taken by sameer = x,
Time taken by abhay = x + 2,
Speed of Abhay = y.
y = 30/x+2.
2y = 30/x -1.
as 30 i.e distance is constant,
xy + 2y = 2xy - 2y.
x = 4,
putting x = 4 in xy + 2y = 30,
y = 5.

@All.


Here, is my explanation;

When Abhay moves at normal speed;

Let the time taken by Sameer, time = X.
Then, Abhay needs 2 more hours time than Sameer. ie...time=X+2.
Consider the speed of Abhay, speed =Y

Now, Abhay moves at double speed, so he reaches 1 hour before Sameer.

So speed becomes speed=2Y and time =X-1

Now you can make the equation for distance
Distance is already given d=30

Case 1 (during the normal speed of Abhay)
Distance =speed*time
ie...30=Y*(X+2)----> equation 1

Similarly,
Case 2(during the double speed of Abhay)
30=2Y*(X-1)--->equation 2

Now solve equations 1 and 2 with your logic;
You, will get the answer 5.

We know that,
1st case ---> (1)
If Sameer takes 2 hours,
Then, Abhay takes 4 hours.

So,
Sameer takes 2 * 60 = 120 seconds.
&Abhay takes 4 * 60 = 240 seconds.

2nd case ----> (2)
Abhay takes 1hour less than Sameer,
So,
2-1 = 1 * 60 = 60seconds

So,
Abhay's speed is
Case(1)&(2)
240 + 60 = 300Seconds;
Then 300/ 60 = 5.

@All.

Here is the explanation:

Let speed of Abhay = t1.
and speed of Sameer = t2.
t1 = t +2 (t is actual Speed).
t2 = t -1 (t is actual speed).
t1 - t2 = t+2 - (t - 1) = 3.
30/x - 30/2x = 3.
30 - 15 = 3x.
15 = 3x.
x = 5 kmh^-1.

Abhay takes 2 hrs more than Sameer to cover 30 km.
Abhay's speed (s) = 30/t+2 ---> (1)

If Abhay doubles his speed he takes 1 hr less.

Abhay's double speed (2s) = 30/t-1 ---> (2)

Equate (1) and (2) we get,
2[30/t+2] = 30/t-1.
t = 4 hrs.
T = t+2 = 4+2 = 6 hrs.
S = 30/6 = 5 km/hr.