Aptitude - Time and Distance - Discussion

Let us assume first that the velocity of Abhay is V km/hr and say Sameer takes x hours to cover the distance 30km.

Now, we all know S = V*t
=> 30 = V*(x + 2) ; where (x + 2) is the time taken by Abhay to cover the distance 30 km with speed Vkm/hr.

For the second case, i.e, for V' = 2*V, the double speed of Abhay

The above relation changes to:
30 = V'*t = (2*V)*(x-1); where (x-1) is the time taken by Abhay to cover 30km.

Now equating both equations :
=> V*(x+2) = 2*V*(x - 1).
=> x + 2 = 2*x - 2
=> x = 4
Putting x=4 in any of the above two equations we get the velocity V=5 km/hr.

I still not understand how 3 came? Explain in a simple manner please.

Let the time is taken by Sameer to cover 30 km be t. Abhay will take t+2 time to cover the same. If he doubles speed he takes t-1 time.

We know time = distance/speed.

So t+2 = 30/x. Where x is the speed of Abhay? t-1 = 30/2x. Now subtract both sides you can get the solution for x.

@Devi.

Superb and clear explanation, Thanks.

Why can the two equations not be just divided, you'll be able to cancel all unwanted constants and find time directly, but it gives a different answer.

30/x = t + 2
30/2x = t - 1

Dividing both (30/x) / (30/2x) = (t + 2)/(t - 1).
t = 4.

Thank you, very clear solution @Devi.

Good explanation Thank you, @Devi.

30/x - 30/2x = 3.
30/x - 15/x = 3.
15/x = 3.
15/3 = x.
5 = x.

Abhay takes 2 times more than Sameer
2x = x.

If Sameer doubles his speed, he would take less than 1hour of Sameer
2 * 2x = 1 - x,
4x = 1 - x,
4x + x = 1,
5x = 1,
x = 1 ÷ 5.
According to question, speed is 1 ÷ 5 is 5.

Nice explanation & well said @Anand.