Write a system of equations for the problem, and then solve the system.
-At the beginning of a bicycle ride, Raul and Miguel are 132 miles apart. If they leave at the same time and ride in the same direction, Raul overtakes Miguel in 6 hours. If they ride toward each other, they pass each other in 2 hours. What are their speeds?
A) Raul: 44 mph; Miguel: 22 mph
B) Raul: 45 mph; Miguel: 21 mph
C) Raul: 45 mph; Miguel: 22 mph
D) Raul: 22 mph; Miguel: 44 mph

Question

Quizplus · Accepted Answer

When riding in the same direction, the difference in their speeds is the rate at which the distance between them changes. In 6 hours, Raul catches up to Miguel, meaning the difference in their speeds is $132 \, \text{miles} \div 6 \, \text{hours} = 22 \, \text{mph}$. When riding towards each other, their combined speeds equal the rate at which the distance between them decreases. In 2 hours, they meet, meaning their combined speeds equal $132 \, \text{miles} \div 2 \, \text{hours} = 66 \, \text{mph}$. Solving the system of equations formed by these conditions gives Raul's speed as 44 mph and Miguel's speed as 22 mph.

Write a System of Equations for the Problem, and Then