The graph represents the distance in miles, y, that Car A travels in x minutes. The function y = 56
x represents the distance, y, that Car B travels in x minutes. Both cars are moving at a constant rate of speed. Which BEST compares the rates of the two cars?
Responses
A. The rate of Car B is 16
of a mile per minute greater than the rate of Car A.The rate of Car B is 1 6 of a mile per minute greater than the rate of Car A.
B. The rate of Car A is 12
of a mile per minute less than the rate of Car B.The rate of Car A is 1 2 of a mile per minute less than the rate of Car B.
C. The rate of Car B is 16
of a mile per minute less than the rate of Car A.The rate of Car B is 1 6 of a mile per minute less than the rate of Car A.
D. Car A and Car B are traveling at the same rate per minute.
D. Car A and Car B are traveling at the same rate per minute. This is because both cars have a constant rate of speed and their distances are represented by the same formula with the same coefficient (56).
D. Car A and Car B are traveling at the same rate per minute.
To compare the rates of the two cars, we need to analyze the given function equations for Car A and Car B.
The function for Car A is y = 56x, where y represents the distance traveled in miles and x represents the time in minutes.
The function for Car B is y = 1x, where y also represents the distance traveled in miles and x represents the time in minutes.
In both cases, the distance traveled is directly proportional to time, indicating a linear relationship.
Now, let's compare the coefficients of x in both functions. The coefficient in Car A's function is 56, whereas the coefficient in Car B's function is 1.
Since Car A has a coefficient of 56, this means that Car A is traveling at a faster rate than Car B. Therefore, Car A's rate is greater than Car B's rate.
Now let's determine the difference in rates by calculating the difference in coefficients. The difference between 56 and 1 is 55.
Since Car A has a rate that is 55 times greater than Car B, we can conclude that Car B's rate is 1/55th of Car A's rate.
Therefore, the correct response is:
C. The rate of Car B is 1/55 of a mile per minute less than the rate of Car A.