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Question
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.
For this situation, we will analyze the given responses based on Daniel's journey information:
Daniel is traveling a total distance of 450 miles at an average speed of 50 mph.
He drives for 5 hours, which means he covers the following distance in the first part of the trip:
Distance = Speed × Time
Distance = 50 mph × 5 hours = 250 miles
This leaves him with:
Total distance - Distance covered in the first 5 hours = Distance left
450 miles - 250 miles = 200 miles to cover after lunch.
For the remaining part of the trip, we use the variable x to represent the hours he drives after lunch. He's still traveling at the same average speed of 50 mph. Therefore, the distance he covers after lunch is given by:
Distance after lunch = Speed × Time after lunch
Distance after lunch = 50 mph × x hours
Now we examine each response:
A. 50x + 5 = 450
This equation doesn't make physical sense since it adds distance (on the left, represented by 50x) with a small number (5) that doesn't correspond to the remaining distance to be covered or the time driven.
B. 50(x + 5) = 450
This equation properly represents the total distance driven. x represents the time driven after lunch, and 5 represents the time driven before lunch. So the total time driven is x + 5 hours, at 50 mph for a total distance of 450 miles.
C. 50x + 250 = 450
This equation takes into account the distance covered in the first 5 hours (250 miles) and adds it to the distance Daniel needs to cover after lunch (50x miles). This is the correct way to represent the situation as well since it mirrors the remaining distance that needs to be covered (450 miles total minus 250 miles already covered).
D. The total time for the entire trip is 6 hours.
This statement cannot be correct given the information since Daniel has already driven for 5 hours and will continue driving for an unknown additional amount of time x after lunch.
E. The total time for the entire trip is 9 hours.
This statement is not necessarily correct since we don’t have enough information to determine the value of x and calculate the total time for the trip.
Correct statements: B and C.
The total time for the entire trip (5 + x hours) can only be found if x is known. Given the equation 50x + 250 = 450, we can solve for x:
50x = 450 - 250
50x = 200
x = 200 / 50
x = 4
So the total driving time is 5 hours before lunch + 4 hours after lunch = 9 hours. But this calculation wasn't provided in the initial information, only derived from solving the equations, making B and C the only correct responses based on the given information.