Aptitude - Time and Distance - Discussion

Convert km/h to m/s.

S(c) = 75000/T -->(1)
S(tr) = 75000/(T-12.5x60)-->(2)
S(tr) = 3/2S(c) -->(3)

Sub (3) in (2).
3/2s(c) = 75000/(T-12.5x60).

sub (1) in above;

(3/2).(75000/T) = 75000/(T-12.5x60).
T = 3x12.5x60 ---->(4)

Sub (4 in (1) [to get the speed of the car].
S(c) = (75000/3x12.5x60 ).(18/5).
s(c) = 120km/h.

Let the speed of the car be x km/hr.

The train travels 50% faster than the car, so its speed is;
1.5x km/hr.

Travel time of car = 75/x hours.

Travel time of train = 75/1.5 x hours = 50/x hours (time=distance/speed).

But the total travel time taken by train is;

The train lost 12.5 minutes (which is Equal to 12.5/60 hour=5/24 hour) due to stops.
Hence, the total time for the train is the Total time taken by the train = 50/x + 5/24 hour.
In a question given that;
Both the car and the train reach point B at the same time.

Therefore:
75/x = 50/x+50/24.
75/x-50/x = 50/24.
25/x = 50/24.
Solve for x by cross-multiplying.
X = (25*24)/5.
X = 120km/hr.

Train 50% faster so,
Tr:ca = 150:100(or) 3 : 2,speed
Train 12.5 min.
So ,3 * (12.5/60) = 12.5/20,time
Distance = 75
Speed = distance ÷ time.
Speed = 75 ÷ (12.5/20)
Ans : 120 km/hr.

Speed of car = Sc ; speed of train = St.
Sc : St = 100:150 ( A train can travel 50% faster than a car)
= 2:3 -----> (1)
And therefore Tc:Tt= 3:2 -----> (2)

Delay given= 12.5 min = 12.5/60hrs.
Therefore time for car, Tc= 3 * 12.5/60 = 12.5/20 (refer (2)Tc : Tt = 3:2 )
The distance given 75km.
We know, Speed= Distance/Time.

Therefore, the speed of the car,
Sc = 75/(12.5/20),
= 120 km/hr.

150/100 came because train is 50% faster
So, first find the 50% of 100 = that is 50.
Now add the 50 to the total 100% of car = 150.

The ratio of speeds of train and car is 1.5 : 1

Therefore the ratio of time taken by them to cover the same distance is 1 : 1.5

The train lost 12.5 mins while stopping at stations. This means if the train didn't stop at stations it would reach the destination early by 12.5 mins.

That means the difference between the time taken by train and car is 12.5 mins.

Let consider x as the time taken by train.
Then as per the time taken ratio 1 : 1.5, the difference between 1.5x and x is 12.5 mins,
Then x = 25 mins,
Then 1.5 x = 37.5 mins.

Now the car traveled 75 kms in 37.5 mins,
The speed of car is 75/37.5 kms per min.
Speed of car = 75000/2250 m/s
i.e., 100/3 m/s.
Converting m/s into km/hr-
i.e., (100/3) * (18/5) = 120 kmph.

How 150 came? Please explain to me.

Anyone, please explain how can be the term (150/100) mean?

Let time is t.
Suppose Car is going at speed x,
Train speed will be x+(x/2) = 3x/2 -------> 1
Speed of Train(dist/time) = 75/(t-12.5) ------> 2
1 =2.
3x/2 = 75/t ----->3
Speed of car = 75/t.
x = 75/t ----> 4.
substitute 4 in 3.

By solving you get;
time of car(t) = 37.5(in min)
By converting into hr.
t = 0.625 hr.
Speed of car = 75/0.625.
Ans : 120kmph

T:C ( speed) = 3:2.
T:C ( time) = 2:3.
Time taken by car = 12.5× 3.
Speed of the car = 120 km/h.