Aptitude - Time and Distance - Discussion

Time taken for car - time taken for train = 5/24 hr.

This equation is derived because both start at same time and end at same time.

Hi guys let me explain in this way.

Given that both reached the distance 75 km at the same time.

That indicates the time taken by car is equal to the time taken by train.

However the time taken by train also includes the delay times due to stations.

Thus,

Train time = distance/speed + 12.5 min (total time).

Cars time = distance/speed (total time).

As distance = 75 km it is clear but.

The speed of train is 50% faster, means 50% more.

If car speed = S then 50% more is.

S+(50/100)S.

Substitute the equation and you can see the answer your self.

Hi, Actually we get speed as 25 only since.

Speed = Distance/(Time x Extra time).

Speed = 25/(125/600) => (25 x 24)/5 = 120.

Let car speed = x*100%.
= x * (100/100) = x kmph. // just for understanding

Train is 50% more than car
So train speed = x*(100+50)/100 = 150x/100 = 3x/2 kmph.

In the second step. Let us consider an example a train can reach the destination without stopping at the stations in 10 mins. So the actual time is 10 mins. If it takes extra 2 mins while stopping at the stations. So 10+2=12 mins.

A car if totally takes 12 mins to reach the destination. Train Time taken by train i.e. 12 mins = Time taken by car i.e. 12 mins //Both takes equal time.

10(actual time)+2(extra time) //train = 12 //car.

12-10 = 2 ---->1

NOW COMPARING 1 with our problem. The Extra time taken for the train is given that is 12.5 mins.
Hence the equation will be:
(time taken by car) - (actual time taken by train) = extra time taken by the train.

75/x -75/(3x/2) = 12.5/60.

Since we don't know the time taken by car. Time = distance/speed. So, 75/x similarly for train as 75/(3x/2).

So 75/x -75/(3x/2) = 12.5/60. By solving get the x.

Can anyone please explain me this solution easily?

Actually it is 50% more.

i.e (100% + 50 %) * x.

((100/100) + (50/100)) * x.

(1 + (50/100)) * x.

(150/100) * x.

Since the train is 50% faster than than the car and also delayed for 12.5 minutes,

It implies it would have used the time delayed to cover half of the distance=75/2 km.

Therefore its speed =180 km/hr (75/2*60/12.5).

Since trains' speed assuming x to be the speed of the car,

Then x + 0.5x = 180 km,

Thus x = 120 km/hr.

150/100 come using this strategy.

<-------------simple logic:------------->

Suppose car speed =x km/hr.

Then train speed= x + 0.5x.

1.5x or 150/100 or 3/2.

{0.5x comes by breaking the 1x into half (50%) i.e 1/2 i.e 0.5}.

75/x - 75/(3/2)x is in KMPH and the term 12.5 mins is converted into secs. how could the answer can be given in KMPH by equating these two terms? please anyone who knows the explanation, explain me?

train lost 12.5 min , convert into hrs = 12/60 = 1/5.

Remaining time = 4/5.

4/5*75 = 60.

As it is 50% then total speed of car is 120.