Aptitude - Time and Distance - Discussion

Please explain how 3 comes shortly?

Superb explanation devi, anoo, amit sakshi.

Lets abhays speed x km/hr and sameer takes T hour to complete 30 km journey
X=30/T+2

2X= 30/T-1

THEN 2(30/T+2)=30/T-1
2T-2=T+2
T=4 hour
X= 30/T+2
30/4+2= 5 HOURS

Thanks Abdus :).

Thanks Devi

Good explanation Devi.

Another Method.

Let Abhay's speed :- x kmph
Let Sameer's speed:- y kmph

According to the question

30/x - 30/y = 2 -- 1st equation

&

30/y - 30/2x = 1 -- 2nd equation

Solving above two we get:-

(y-x)/xy = 1/15 --3rd equation

&

(2x -y)/xy = 1/15 -- 4th equation

since the rhs of both the equations is equal equating the lhs of the both equations is also correct: so

y -x = 2x - y

i.e

2y = 3x or y = 3x/2

now equate the value of y in 3rd or the 4th equation as follows:-

(2x - (3/2)x)/(x*(3/2)x) = 1/15

we get

x/3x^2 = 1/15

so

1/x = 1/15

so

x = 5 km/hr

Hope this helps.

The solution may be found with 2 variables, explained nicely above with x and y.

However, the above solution is done with 1 variable only.

The figure of 3 comes from the total savings in hrs if the speed is doubled.

Assuming Abhay's speed is = x ; time taken is 2 hrs more
If Abhay's speed is doubled = 2x ; time saved is 1 hrs more

Therefore difference in speed results in total time savings = 3 hrs (2 hrs + 1 hr)

Now, to calculate the two speeds:

Given distance = 30 km
Assuming Abhay's speed = x
Therefore Time1 = 30/x

Abhay's speed is doubled = 2x
Therefore Time2 = 30/2x

Since difference in time is the total time saved :
Hence,

Time1 - Time2 = 3 hrs

30/x - 30/2x = 30

Solving :
6x = 30
x = 5 kmph

Let us look at ths prb this way:
Let abhays's speed be x and sameers time be y
Case 1: Abhays speed=x
Abhays time =t+2

Case 2: abhays speed=2x
Abhays time =t-1
We knw : Speed is inversely proportional to time
So, S2/S1=t1/t2
2x/x=t+2/t-1

2=t+2/t-1
solving we get t=4
hence we can calculate
Speed of abhay=Distance/time
=30/(4+2) ..Since t=4
30/6=5

If sameer take 5hr than abhay take 7 hr
when he increases his speed double than he take 4hr hence different is 7-4=3
mean (30/x)-(30/2x)=3(solve)
30/x speed when he take more time,30/2x when he double his speed
hence diff. between them=3

Thanks devi. You made it simply.