Aptitude - Time and Distance - Discussion

For every 10km he walked, he walked an extra 4km.

So the question is, if he walked an extra 20 km, what would be the actual distance he covers?

Then 10 × 20/4 = 50.

Speed of train: speed of car = 150: 100 = 3: 2.

(As speed is inversely proportional to time)
Train time: car time = 2 : 3.
1 part = 12.5min, 2part = 25min, 3part = 37.5min.
Convert it into hr 375/600 = 5/8 hr.

Speed = distance/time.
Speed of car = 75/(5/8) = 75 * 8/5 = 120km/hr.

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.