I have a question about a College Algebra word problem.

Question

Syracuse and New York are 240 miles apart. one car left Syracuse for New York, averaging 65 mph. at the same time, another car left New York for Syracuse, averaging 55mph. how far from Syracuse did the cars pass each other? step by step answer. 

Answer 1

Distance = (Rate)(Time), so Time = Distance/rate

 

Let x = distance of first car from Syracuse when the cars pass each other

 

Then 240 - x = distance of second car from Syracuse at that time

 

When the cars pass, their travel times are equal.

 

So, x/65 = (240-x)/55

 

Cross multiply to get 55x = 65(240-x)

 

                             55x = 15600 - 65x

 

                            120x = 15600

 

                                 x = 130 miles

 

The cars pass when the first car is 130 miles from Syracuse and the second is 110 miles from NYC (or, in 2 hours after the cars departed from their respective starting points).