Aptitude - Time and Distance - Discussion

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.

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.

Why do we have to subtract the speed of a car - the speed of a train?

Please explain to me

Can anyone explain to me, how 12.5/60 9is = 5/24?

150/100 came because;
Car speed is 100% and train speed is 50% faster than a car so,
Car speed (100/100)+(50/100),
=(1/1)+(50/100),
Cross multiply then (100+50)/100.
= 150/100.

Train : car = 150:100 or 3:2.
Difference = 12.5 so 1 part is 12.5.
Speed and time is vice versa.
Time = train : car is 25 min : 37.5 min.
37.5 min = 75 kmph.
60 min = 120 kmph.

Thanks for explaining the answer @VIJETH BK.

If the car speed is 100kmph then the train speed is 150 kmph.
Because train 50% extra speed than a car.

Train in station stopping time is 12.5min.
But a car and train cover the same distance.
In case the train running non-stoping train cover more distance.
car: train 100%:150%.
car : train 100% ====(100% + 12.5min)

That 50% is 12.5min.
100% = 2 * 12.5min.
100% = 25min..
37.5min =75kmph
1min = 75/37.5
1min = 2 kmph
1hour = 60min = 2 * 60 = 120kmph.

The speed of the train: speed of the car = 150 : 100 = 3 : 2.
From the formula ; ratio of the speed = a:b,
if the same distance then, ratio of the time = b : a
Time ratio = 2:3
1u = 12.5 min
2u = 25 min
3u = 37.5 min.

The time taken by the car in hr = 37.5/60 = 375/600,
= 5/8 hr.
SPEED OF THE CAR IS = 75 divided by 5/8.
= 15 * 8.
= 120 km /hr.

The speed of car be x km/h.
Then speed of the train will be = 3x/2km/h,
and the time taken to cover up 75 km is equal, but the train lost about 12.5 minutes while stopping at the stations.
So 75/x - 50/x = 5/24,
x= 120km/h.