Please help me!!!!-tel & explain the answer

I think answer is B.

What is OA?

IMO D

Info given:

Train A speed = 100 mph
A leaves NY at 3:00PM
The 2 trains meet after 1 hr at 4:00PM

Train B leaves Boston at 3:50PM
Ta+Tb=2hrs
(Ta-time taken by A; Tb time taken by B)

Let speed of train B = S
Total distance between NY and Boston = D

Distance between NY and point of meeting = 100mph*1hr = 100miles (Speed of A*time taken)

Hence D = 100+X

X is the distance covered by train B from Boston to meeting point

X=S*10/60=S/6

(10/60 is the time taken by train B to reach meeting point (MP) in hours. B started at 3:50PM and reached meeting point at 4PM. Hence the total time taken to reach MP = 10mins)
D=100+S/6
D=(600+S)/6 -----equ1

Ta+Tb=2

(D/100) + (D/S) = 2-----equ2

Sub. The value of D in equ2.

(600+S)/600 + (600+S)/S = 2

Simplify to get the equ: S^2-500S+60,000=0
Solving for S we get S= 300, 200

When S=300 D=150
When S=200 D=800/6
St 1 Train B arrived in New York before Train A arrived in Boston.

Tb>Ta

When S=300 and D=150 (sub S in equ 1 to find D)
Ta = D/100 = 4:30pm
Tb = D/S = 4:20pm ---- Tb>Ta satisfies the condition

When S=200 and D=800/6
Ta=D/100=4:20pm
Tb=D/S = 4:30pm------Ta>Tb does not satisfy the condition

Hence Tb=4:20pm St 1----SUFF

St 2 The distance between New York and Boston is greater than 140 miles.

I.e. D>140miles

D=150miles, S=300 and Tb=4:20pm

St 2----SUFF

Answer is D

I really apologize for the length of the soln but I couldnt find a shorter way to explain the problem
The ques was a real monster.