Okay, so I need to figure out how far a car would travel at 50 miles per hour in 2 and 3/4 hours. Hmm, let's start by recalling the basic formula for distance. I think it's distance equals speed multiplied by time. Yeah, so distance = speed × time. That makes sense. So if the car is going at 50 mph and the time is 2.75 hours (since 3/4 is 0.75), then the distance should be 50 times 2.75. 

Wait, but the problem asks for the answer as a mixed number. Mixed numbers are like 2 3/4, not decimals. So maybe I should keep the time as a fraction instead of converting it to a decimal. Let me think. 2 and 3/4 hours is the same as 11/4 hours. Let me check that: 2 is 8/4, plus 3/4 is 11/4. Yes, that's right. So 11/4 hours. So then, distance would be 50 multiplied by 11/4. 

Let me write that out: 50 × (11/4). To compute this, I can multiply 50 by 11 first, which is 550, and then divide by 4. 550 divided by 4. Let's see, 4 goes into 550 how many times? 4 × 137 is 548, so 137 with a remainder of 2. So 550/4 is 137 2/4, which simplifies to 137 1/2. So the distance is 137 and a half miles. 

Wait, let me verify that again. If the car is going 50 mph for 2 hours, that's 100 miles. Then for the additional 3/4 of an hour, which is 45 minutes, it would go 50 × 0.75 = 37.5 miles. Adding those together: 100 + 37.5 = 137.5, which is the same as 137 1/2. So that checks out. 

Another way to compute 50 × 11/4: 50 divided by 4 is 12.5, and 12.5 × 11. Let's do that. 12 × 11 is 132, and 0.5 × 11 is 5.5, so 132 + 5.5 = 137.5. Yep, same result. 

So both methods give me 137.5 miles, which is 137 and a half miles as a mixed number. Therefore, the answer should be 137 1/2. 

Wait, just to make sure I didn't make any calculation errors. Let me redo the multiplication: 50 × 11/4. 50 ÷ 4 = 12.5, then 12.5 × 11. 12.5 × 10 is 125, plus 12.5 × 1 is 12.5, so 125 + 12.5 = 137.5. Correct. 

Alternatively, 11/4 is 2.75, so 50 × 2.75. 50 × 2 is 100, 50 × 0.75 is 37.5, 100 + 37.5 is 137.5. Yep, all methods lead to the same answer. 

So the final answer, expressed as a mixed number, is 137 1/2 miles. That seems right. I don't think I made any mistakes here. The key was converting the mixed number time into an improper fraction or decimal and then multiplying by the speed. Both approaches worked well. 

Just to recap: The formula distance = speed × time is fundamental here. Converting the mixed number time to an improper fraction made the multiplication straightforward. Then simplifying the result back to a mixed number gave the answer. Alternatively, breaking down the time into whole hours and fractions of an hour also worked. Both methods confirmed the same result, so I'm confident the answer is correct.
Therefore, the car would travel $\boxed{137\frac{1}{2}}$ miles in $2\frac{3}{4}$ hours at a speed of 50 miles per hour.
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