Question

A train Express A leaves Delhi at 5 a.m and reaches Mumbai at 9 a.m.Another train Express B leaves Mumbai at 7 a.m and reaches Delhi at 10.30 a.m.At what time do they cross each other after 7 a.m ?​

Answer 1

Answer:

7:56 am

Step-by-step explanation:

Let’s denote the first train as T1 and second train T2. And the subsequent rate and time we denote with similar subscript.

At first, let’s get done with the low hanging fruits. The rate/speed of two trains. Assuming the total distance between Meerut and Delhi = d.

For T1:

time = 4 hours (5:00AM to 9:00AM)

speed = d/4

For T2:

time = 3 + 1/2 = 7/2 hours (7:00AM to 10:30AM)

speed = 2d/7

Since the unit of speed are redundant here, let’s leave those out.

Now, think about the starting time of T1, 5:00 AM,

the starting time of T2, 7:00 AM

Notice that T1 has a 2 hours head start. In this 2 hours time T1 must have traveled:

= d/4 * 2 (rate * time = distance)

= 2d/4 = d/2

So, T1 covered half the distance in those 2 hours.

At this moment T1 and T2 are at the point with a distance of d/2 between them and both are at 7:00AM. Think about it, if we can find the time taken by either T1 or T2 after 7:00AM up to the time they meet, then we can add that hour/minutes to 7:00AM and find out the exact clock time when they meet.

Let’s assume that, they meet after t hours i.e. (7:00 + t) AM would be the time they meet. Observe that the value of this t is same for both T1 and T2. Since, the time they will meet each other has to be same for both. Moreover, both of them are now at the 7:00AM point.

We assume that from a distance of x from the point of T1, they will meet.

This inevitably makes the distance from T2: d/2 - x. (distance between them is now d/2)

So, from the perspective of T1:

t = distance/rate = x / (d/4) = 4x/d

From the perspective of T2:

t = distance/rate = (d/2 - x) / (2d/7) = (d/2 - x) * (7/2d)

We can equate these two as:

4x/d = (d/2 - x) * (7/2d)

Finding the value of x here:

= 7d/30

Observe, this is the distance that is covered by T1 at the time of meeting with T2. As we already know the rate/speed of T1, we can easily find time:

time = distance / rate = x / (d/4)

Replacing the value of x from above, we get:

time = 14/15 hour = (14/15) * 60 minutes = 56 minutes

Therefore, t = 56 minutes. As we mentioned earlier, (7:00 + t) AM will be the time of their meeting.

After 56 minutes, starting from 7:00AM, they will meet.

So, at 7:56 AM the two trains will meet!

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