Aman welcome back to the forums...

difference is speeds is 10
say the distance is X

then
(X/8)-(X/10)=10
solve the equation=>X=400
now
total distance/total time = average speed
(400+400)/(10+8)
=400/9
=44.44 (trick here is 1/9 is 0.111*)

My approach is this:

Lets assume

Train 1 - Leaves @ 6 AM whose speed is S1 and time taken is T1
Train 2 - Leaves @ 8 AM whose speed in S2 and time taken in T2
Distance - D between Connecticut and New York


Step 1:

Make an equation.

The speeds of the two trains are:

S1 = D/T1 => S1*T1=D -- 1st Equation

S2 = D/T2 => S2*T2=D -- 2nd Equation

Since both the trains travel the same distance lets equate Equation 1 and Equation 2

S1*T1=S2*T2


Step 2:

Train 1 takes 10 hours to reach NY => T1=10
Train 2 takes 8 hours to reach NY => T2=8

Let the speed S1 of the train1 be x.
So the speed S2 of the train2 will be x+10 (As per the info provided in the question)

x*10=(x+10)*8

=>10x=8x+80
=> 2x=80
=> x=40

So,
S1=x=40 kmph and
S2=x+10=50 kmph


Step 3:

Now we need to calculate the average speeds of both the trains.
(Though this question looks like Time, Speed Distance question at the first glance, it is actually a weighted average question)

Train 1 travels @ 40 kmph for 10 hours => 400 kms
Train 2 travels @ 50 kmph for 8 hours => 400 kms

Train 1 and Train 2 together take 18 hours to travel 800 kms

So, the average speed of both the trains is

(400+400)/18 = 44.44 kmph