Daniel is traveling 450 miles at an average speed of 50 mph to a job interview. He drives for 5 hours, stops for lunch, and resumes driving for x hours to the interview. Choose ALL correct statements for this situation.
Responses
A 50x + 5 = 45050x + 5 = 450
B 50(x + 5) = 45050(x + 5) = 450
C 50x + 250 = 45050x + 250 = 450
D The total time for the entire trip is 6 hours.The total time for the entire trip is 6 hours.
E The total time for the entire trip is 9 hours.
A, B, and D are the correct statements for this situation.
Statement A is correct because the equation 50x + 5 = 450 represents the total distance traveled (50x) plus the initial 5 hours of driving (5) equaling the total distance of 450 miles.
Statement B is correct because the equation 50(x + 5) = 450 represents the average speed (50 mph) multiplied by the total time spent driving (x+5) equaling the total distance of 450 miles.
Statement D is correct because the total time for the entire trip includes the 5 hours spent driving initially and the additional time spent driving to the interview. The lunch break is not included in the total time.
To solve this problem, let's break down the information given and analyze each statement:
Statement A: 50x + 5 = 450
This equation is incorrect since we are trying to find the value of x, the time for the second part of the trip, and not the equation that equates to 450.
Statement B: 50(x + 5) = 450
This equation is correct. It represents the total distance traveled, which is the sum of the distance traveled in the first part (50 mph for 5 hours) and the second part (50 mph for x hours).
Statement C: 50x + 250 = 450
This equation is incorrect since 250 is not the correct representation of the first part of the trip. It should be 50 mph for 5 hours, not 250.
Statement D: The total time for the entire trip is 6 hours.
This statement is incorrect. The total time for the entire trip is the sum of the time spent in the first part (5 hours) and the time spent in the second part (x hours).
Statement E: The total time for the entire trip is 9 hours.
This statement is incorrect. We do not have enough information to determine the total time for the entire trip.
Therefore, the correct statements are B: 50(x + 5) = 450 and D: The total time for the entire trip is 6 hours.
To solve this problem, we need to use the formula distance = speed × time.
We know that Daniel drives for 5 hours at an average speed of 50 mph. Therefore, the distance traveled during this time is 50 mph × 5 hours = 250 miles.
The remaining distance to the job interview is 450 miles - 250 miles = 200 miles.
We want to find the time it took Daniel to drive the remaining distance of 200 miles at an average speed of 50 mph. Let's call this time x hours.
So, the correct equation to represent this situation is: 50x = 200.
Let's break down the options:
A. 50x + 5 = 450: This equation does not correctly represent the situation because it involves the total distance traveled, which is 450 miles, instead of the remaining distance.
B. 50(x + 5) = 450: This equation does not correctly represent the situation because it involves the total distance traveled, which is 450 miles, instead of the remaining distance.
C. 50x + 250 = 450: This equation correctly represents the situation because it involves the remaining distance of 200 miles, which is equal to 50x. Adding the previously traveled distance of 250 miles gives the total distance traveled.
D. The total time for the entire trip is 6 hours: This statement is incorrect because the total time for the entire trip would be 5 hours driving + x hours driving to the interview, which is not necessarily equal to 6 hours.
E. The total time for the entire trip is 9 hours: This statement is incorrect because the total time for the entire trip would be 5 hours driving + x hours driving to the interview, which is not necessarily equal to 9 hours.
Therefore, the correct statements are:
C. 50x + 250 = 450
D. The total time for the entire trip is 6 hours.