Question

shramjeevi express leaves patna for new delhi at 10 : 10 am and reaches new delhi at 3 : 30 pm. magadh express leaves new delhi at 9 : 48 am and reaches patna at 2 : 36 pm. if routes of both the trains are the same, then at what time will both the trains meet each other ?

Answer 1

Time taken by Shramjeevi express = 5 hours 20 minutes = 320 minutes

Time taken by Magadh express = 288 minutes

Let the total distance = d

Since, Distance = Speed X time taken

Speed of Shramjeevi express = $\frac{D}{320}$

Speed of Magadh express = $\frac{D}{288}$

Since, Magadh starts 22 minutes before Shramjeevi express,

Therefore, distance covered by Magadh in 22 minutes = $\frac{22D}{288}$

Let after 't' minutes both the trains meet each other.

So, distance covered by both the trains in 't' min plus distance covered by Magadh in previous 22 min will be equal to 'D'.

Therefore,

$\frac{22D}{288}+\frac{tD}{288}+\frac{tD}{320}=D$

Cancelling D from both the sides of the equation.

The LCM of 288 and 320 is 2880.

$\frac{220+10t+9t}{2880}=1$

$220+19t = 2880$

19t = 2660

t = 140

Therefore, after 140 minutes that is 2 hours and 20 minutes after 10:10 am, both the trains will meet each other.

Therefore, at 12:30 pm both the trains will meet each other.

Answer 2

Time taken by Shramjeevi=320 min

Time taken by Magadh=288 min

Let total distance= D

So, speed of Shramjeevi Vs=D/320

Speed of magadh Vm=D/288

Magadh starts 22 min before Shramjeevi.

So, distance covered by magadh in this duration = 22*D/288

Now let after 't' min both the trains meet.

So distance covered by both the trains in 't' min plus distance covered by magadh in previous 22 min will be equal to 'D'.

Mathematically,

t + 22 = D

From here, t=140

Thus after 2 hours and 20 min (after 10:10 AM) both the trains will meet i.e. at 12:30 pm.