Question 459737
Students are traveling in two cars to a football game 135 miles away. The first car leaves on time and travels at an average speed of 45 miles per hour. The second car starts 1/2 hour later and travels at an average speed of 55 mile per hour. How long will it take the second car to catch up to the first car before the first car arrives at the game? 

Let x = the number of hours it will take the second car to catch up to the first car before the first car arrives at the game

To catch-up, the second car must travel the same distance as the first car.

Where:
55x      = distance traveled  by the second car
45(x+.5) = distance traveled  by the second car

Equation:
55x = 45(x+.5)
55x - 45x = 22.5
10x = 22.5
x = 2.25 or 2 hours and 15 minutes

It will take 2 hours and 15 minutes for the second car to catch up to the first car.