Aptitude - Time and Distance - Discussion

Most Members doubt is how come this speed equation =(3/2)x.
speed =x.

Eg 1:
Car speed =50.
Train speed =>50 + (50/2)=> 50 + 25 = 75
Speed equation => train speed/car speed => 75/50 =3/2.

Ex 2:
Car speed =100.
Train speed =>100+(100/2) => 100 + 50 = 150.
Speed equation =>train speed/car speed => 150/100 = 3/2.

Time equation for train:
However, the train lost about 12.5 minutes while stopping at the stations.
Train's Total Time = Run time + Stopping time.

Convert 12.5 minutes in Hours as follows by 12.5 => 12.5/60 => 125/600 => 25/120 = 5/24.

Want to find the real speed of both the car and the train:
Formula : time = distance/speed.
speed = x.
car = train.
75/x = 75/(3/2)x + 5/24 simplify ->(75/1)*(2/3)->150/3=50/1.
75/x = 50/1x + 5/24 -> 1x and x both are same.
(75/x)-(50/x) = 5/24.
75-50/x = 5/24.
25x = 5/24.
x = 5/24/25, simplify -> (24*25)/5 -> 600/5 -> 120/1.
x= 120/1, don't consider 1.

Answer = 120.

I don't understand. Please explain me in detail.

Speed = Distance/Time.

Step 1 :

If x be the Speed of Car, then Speed of Train is x+50/100 = 3x/2.
According to this problem, Formula can be adjusted as Time = Distance/Speed.

Step 2 :
Time taken by Car => T1 = 75/x.
Time taken by Train => T2 = 75/ 3x/2 => T2 = 50/x.

Step 3 :
However, the train lost about 12.5 minutes while stopping at the stations.
Train's Total Time = Run time + Stopping time.

Convert 12.5 minutes in Hours as follows by 12.5 = 12.5/60
=>125/600 = 25/120 = 5/24.

Train's Total Time = 50/x + 5/24.

Step 4 :
Both reach at the same time, so T1 = T2.
Total time of Car = Total time of Train.
=> 75/x = 50/x + 5/24.
=> 75x - 50/x = 5/24.
=> 25/x = 5/24.
=> 120 = x.
Hence x = 120.

The speed of the car is x km/h.
The speed of the train = x + 50x/100,
= 150x/100,
= 3x/2 km/h.

The time taken by the car = 75/x.
The time taken by the train = 75/(3x/2).

The difference between them is 12.5 minutes.
75/x - 75/(3x/2) = 12.5 minutes.

To convert minutes to hours, divide the number by 60,
Therefore,
75/x - 75/(3x/2) = 12.5/60 hr,
75/x - 75/(3x/2) = 125/(10*60) hr,
75/x - 50/x = 5/24,
25/x = 5/24,
5x = 25*24.
x = 120 km/hr.

The train can travel 50% faster than a car. How to define 150 here? Please explain.

Most of people saying 1/2 instead of 3/2 is wrong.

The train is 50% more means 1/2 and also 1 for the car speed is added, So it's 3/2.

I didn't understand this, anyone please explain to me?

(The train can travel 50% faster than a car).

This means the train is travelling 1/2 time faster than the car, not 3/2 time faster.

Final Answer: Speed of the car = 100 kmph.

Speed of car =2/3 the speed of the train.

ie Vc=2/3 Vt, therefore,
Time taken by car =3/2 Time taken by train ie.Tc=3/2 Tt.
Also,
Tc = Tt+15/60 hr ie. Tc = Tt + 1/4.

Therefore:
3/2 Tt = Tt+1/4
Tt = 1/2 = 0.5 hr.

Therefore, Tc = 0.75 = hr.

Distance = v x t.
75 km = Vc x 0.75,
Vc = 100km
Vt = 120.

I am not understanding this question. Please explain to me.