Aptitude - Time and Distance - Discussion

How come 125 and why divided by 60?

It's 12.5 minutes.

To convert it to an hour it should be divided by 60.
i.e 12.5/60 hrs (or)125/(60*10) hrs.

Train spent extra 12.5 minutes then a car. So we have to subtract bigger time from lesser time to get 12.5. It means that time spent by car must be subtracted from the time taken by car to get the excess time of 12.5 minutes. Thus, it should be like this:

75/(1.5*x)-75/x=0.21 (in hours).

Train speed = 50% faster than car speed.

Train speed = car speed + extra 50 % of car speed.
(car speed = X),
(50% extra of X = X/2),
Train speed = X + X/2 = (X/1 + X/2) = (2X+X)/2;
Train speed = 3X/2.

Here why we used 75/x-75/(3/2)x=125/10*60.
Please anyone can explain me?.

I think there should be 50/100 not 15/100 right?

Actually he gave 50% more not 50% times.
so, the speed of train = speed of car + 50% speed of car.
= x+(50/100)*x = 3/2x.

Given that, time of car - time of train = 12.5 min,
(75/x) - (75/(3/2*x)) =125/10 min,
75/x(1 - (2/3)) =125/(10*60) hrs,
1 = 125x/600,
x = 120 kmph.

The speed of the train is 50% more than a car.
If the car travels at x kmph then 50%of x is x/2kmph.
Note train travels 50% more which means actual x and 50% of x is x/2 together (x+x/2) =3x/2.

Let the speed of car be x.

Since the speed of the train is 50% more than the speed of the car, speed of train will be x+(50% of x).

i.e x+x/2 which is 3x/2.

now, let t be the time taken by car. therefore t=75/x --->eq(1)

(using time= distance/speed).
given that train loses 12.5 mins. therefore the total time travelled by train is t-12.5 min (note that both train and car took the same time to reach B. that's why we can take t as the time taken by both car and train)

using time=distance/speed formula, we will get;

t-12.5=75/(3/2x).
which can be rewritten as t-12.5=75/1.5x ----> eq 2
from eq1, we have x=75/t , sub in eq 2.

t-12.5=75/1.5x.
t-12.5=(75*t)/(1.5*75),
t-12.5=t/1.5,
solving which we get.
t=37.5 min=37.5/60 hrs.

as we have x=75/t (from eq1).
x=(75*60)/37.5,
x=120km/hr.

Anyone explain me from 2nd step.