Question

Syracuse and New York City are 240 miles apart. One car left Syracuse heading for New York City at an average of 65 mph. A second car left New York City heading to Syracuse at 55 mph. How far from Syracuse did the cars pass each other?

Answer 1

Let x be the distance from Syracuse where they pass. The first car travels a distance of x in time x/65 while the second car travels a distance 240-x in time (240-x)/55. They pass at the same time after leaving their starting points so x/65=(240-x)/55.
Cross-multiplying we get: 55x=65(240-x)=15600-65x, 120x=15600, x=15600/120=130 miles.
They pass 130 miles from Syracuse.