The two trains close at a speed of 100+150 mph=250mph. At 250mi/h they will meet after 600mi/250mi/h 2.4 h. At a speed of 150mi/h the train leaving New York will cover (2.4h)(150mi/h)=360mi and the train leaving Chicago will cover 240mi.
fuel used = 8 - 6 = 2 gallons distance travelled (on 2 gallons) = 60 miles. distance that could be travelled on a full tank (8 gallons) = 60mi x 8gal/2gal = 240mi. Think about it: if you can go 60 miles on a quarter of a tank, then you can go four times as far on a full tank. In general, if you go a distance Dusing an amount A of fuel, then with an amount F of fuel you could go a distance M, where M = D x F/A This is a simple application of ratios.