A train leaves Canberra for Sydney at 12 noon and another train leaves Sydney for Canberra 40 minutes later. Both travel at the *same constant* speed. The time taken by each to complete one trip is 3.5 hours.

Let the distance between the stations be D and the time after 12 that they meet is x hours. As they complete one trip in 3.5 hours their speed is `D/3.5`

Distance = speed*time; the time traveled by the train leaving Canberra is x and the time traveled by the other train is `x - 40/60` hours.

`(D/3.5)*x + (D/3.5)*(x - 40/60) = D`

Cancel D from both the sides

=> `x/3.5 + x/3.5 - 4/21 = 1`

=> `x*(2/3.5) = 25/21`

=> `x = 25/12` hours

=> x = 125 minutes

**The two trains meet after 125 minutes the first starts or at 2:05 pm**

**In my first answer i have made a mistake by taking 40minutes as 45 minutes. Appologize for that and this gives themodified answer.**

Let distance between canberra and sydney be X km.

The time for this trip = 3.5 hours

Then the travel speed of a train (V) = X/3.5 km/h

Say the trains meets at a distance Y km from canberra. Then from sydney it has (X-Y) km.

If the first train starts its journey at t=0; the second will start its journey at t=2/3h or t=40minutes.

Let the trains meet together at time t= t1

Then at time t=t1

first train has travelled Y km.

But distance = velocity*time

Therefore Y = v*t

** Y=(X/3.5)*t1**-------------(1)

When t=t1 the second train has only traveeled (t1-0.75) h since it was 45 minutes late.

The distance travelled by second train when trains meet together is (X-Y) km.

Then like first train;

**(X-Y) =(X/3.5)*(t1-2/3)**----------(2)

From (1) Y=(X/3.5)*t1

**Y/X = t1/3.5**-------------------(3)

From (2) (X-Y) =(X/3.5)*(t1-2/3)

(X-Y)/X = (t1-2/3)/3.5

(X/X-Y/X) = (t1-2/3)/3.5

1-Y/X = (t1-2/3)/3.5

**Y/X = 1-(t1-2/3)/3.5**----------------(4)

The left side of both (3) and (4) are equal.

Therefore **t1/3.5**= **1-(t1-2/3)/3.5**

t1/3.5= (3.5-(t1-2/3))/3.5

t1= 3.5-t1+2/3

t1 = (3.5+2/3)/2

t1= 2.083333 h

t1 = 2h and 5 min

**So the trains will meet 2 hours and 5 minutes after the first train starts its journey.**

**Assumption**

**Both trains travel at same speed right from the start.**