Write a system of equations for the problem, and then solve the system.
-Two trains start from towns 572miles apart and travel toward each other on parallel tracks. They pass each other 5.5 hours later. If one train travels 18 mph faster than the other, find the speed of each train.
A) 51 mph; 53 mph
B) 56 mph; 48 mph
C) 63 mph; 41 mph
D) 61 mph; 43mph

Question

Quizplus · Accepted Answer

Let the speed of the slower train be $x$ mph and the speed of the faster train be $x + 18$ mph. The total distance covered by both trains when they meet is 572 miles. Since distance = speed $\times$ time, the equation for the slower train is $x \times 5.5$ and for the faster train is $(x + 18) \times 5.5$. Adding these distances gives the total distance: $x \times 5.5 + (x + 18) \times 5.5 = 572$. Simplifying, we get $11x + 99 = 572$, leading to $11x = 473$, and $x = 43$. Therefore, the slower train's speed is 43 mph, and the faster train's speed is $43 + 18 = 61$ mph.

Write a System of Equations for the Problem, and Then