To analyze Daniel's trip, let's break down the key information provided:
- He drives a total distance of 450 miles.
- He drives for 5 hours at an average speed of 50 mph.
- He then drives for an additional x hours.
First, we can calculate the distance he covers in the first 5 hours:
Distance for the first part of the trip = Speed × Time = 50 mph × 5 hours = 250 miles.
Now, let's figure out the remaining distance that he needs to cover after the first 5 hours:
Remaining distance = Total distance - Distance covered in first 5 hours = 450 miles - 250 miles = 200 miles.
Since the average speed is constant at 50 mph, we can find the time it takes to cover this remaining distance. We can use the formula:
Time = Distance / Speed.
So for the remaining distance: Time for remaining distance = 200 miles / 50 mph = 4 hours.
Now, we have the total time for the entire trip:
Total time = Time for first part + Time for second part = 5 hours + 4 hours = 9 hours.
Now, let's evaluate the provided options:
A. \(50x + 5 = 450\)
- This is incorrect because the left side does not accurately represent the relationship of distance travelled in terms of x.
B. \(50(x + 5) = 450\)
- This is also incorrect since it implies that he drives for x hours plus an additional 5 hours continuously, which is not correct in this context.
C. \(50x + 250 = 450\)
- Correct. This sets up the equation where \(50x\) represents the distance he drives after lunch, plus the 250 miles he drove in the first 5 hours equals the total distance of 450 miles.
D. The total time for the entire trip is 6 hours.
- Incorrect. We've calculated the total time to be 9 hours.
E. The total time for the entire trip is 9 hours.
- Correct. We determined that the total time taken for the entire trip is indeed 9 hours.
Thus, the correct responses are C and E.
1 answer