Solve the problem.
-Two cars leave a city and head in the same direction. After 2 hours, the faster car is 22 miles ahead of the slower car. The slower car has traveled 84 miles. Find the speeds of the two cars.
A) 31 mph and 42 mph
B) 110 mph and 121 mph
C) 42 mph and 53 mph
D) 44 mph and 55 mph

Question

Quizplus · Accepted Answer

Let the speed of the slower car be x mph and the speed of the faster car be y mph. 
After 2 hours, the slower car has traveled 2x miles and the faster car has traveled 2y miles. 
We are given that the faster car is 22 miles ahead of the slower car. 
Therefore, 2y = 2x + 22 
Simplifying, we get y = x + 11 
We are also given that the slower car has traveled 84 miles in 2 hours. 
Therefore, x = 42 mph. 
Substituting x in the equation y = x + 11, we get y = 53 mph. 
Thus, the speeds of the two cars are 42 mph and 53 mph. Let the speed of the slower car be x mph and the faster car be y mph.
After 2 hours, the distance traveled by the slower car is 2x + 84 and the distance traveled by the faster car is 2y.
We know that the faster car is 22 miles ahead of the slower car, so we can set up the equation: 2y - (2x + 84) = 22
Simplifying the equation, we get: 2y - 2x - 84 = 22
2y - 2x = 106
y - x = 53
We also know that the slower car traveled 84 miles in 2 hours, so we can set up another equation: 2x = 84
Solving for x, we get x = 42
Substituting x = 42 into y - x = 53, we get y = 95
Therefore, the speeds of the two cars are 42 mph and 95 mph, and the best choice is C.

Solve the Problem. -Two Cars Leave a City and Head in the Same