<Question>
At 50 miles per hour, how far would a car travel in $2\frac{3}{4}$ hours? Express your answer as a mixed number.
</Question>

<think>
<Plan_1>
Okay, let's see. The problem is asking, if a car is traveling at 50 miles per hour, how far would it go in 2 and 3/4 hours? And they want the answer as a mixed number. Hmm, right. So, distance equals speed multiplied by time, right? That's the basic formula. So, distance = speed × time.
So, I need to calculate 50 miles per hour multiplied by 2.75 hours, since 2 and 3/4 is the same as 2.75.

Wait, let me make sure. 3/4 of an hour is 45 minutes, right? Because 1/4 is 15 minutes, so 3/4 is 45. So, 2 hours and 45 minutes. So, the time is 2.75 hours.

So, 50 times 2.75.

But maybe I should do this step by step. Let me think. 2 and 3/4 hours can be written as an improper fraction.
3/4 is 0.75, so 2.75 is the same as 11/4. Wait, 2 is 8/4, so 8/4 + 3/4 is 11/4. So, 11/4 hours.

So, multiplying 50 by 11/4. Let's see. 50 divided by 4 is 12.5, and 12.5 multiplied by 11. Hmm, that might be easier. 12.5 times 10 is 125, and 12.5 times 1 is 12.5, so adding them together gives 137.5.

Alternatively, 50 multiplied by 11 is 550, and then divided by 4. 550 divided by 4.

Let me check that again. 50 × 11/4. 50 × 11 is 550, divided by 4.

<prompt_1.1> Verify the calculation of 50 × 11/4 by breaking it down into simpler steps. </prompt_1.1>

But the question says to express the answer as a mixed number. 137.5 is the same as 137 and 1/2. So, 137 1/2 miles.

Wait, let me confirm once more. 50 mph for 2 hours is 100 miles.
Then, 50 mph for 45 minutes. Since 45 minutes is 3/4 of an hour, so 50 × 3/4 is 37.5. Then, adding 100 + 37.5 gives 137.5, which is 137 1/2. Yep, that checks out.

Alternatively, breaking down the 2 and 3/4 hours into 2 hours plus 45 minutes. Then, calculate each part separately. For the 2 hours: 50 × 2 = 100 miles. For the 45 minutes (which is 0.75 hours): 50 × 0.75 = 37.5 miles. Adding them together gives 100 + 37.5 = 137.5 miles. Same result.

So, converting 0.5 to a fraction, that's 1/2.
Therefore, 137.5 is 137 1/2. So, the mixed number is 137 1/2.

I think that's correct. Let me just verify once more with the fraction method. 11/4 multiplied by 50.
50 divided by 4 is 12.5, multiplied by 11 is 137.5. Yep. So, all methods lead to the same answer.
</Plan_1>

<Execution_1>
<execution_1.1>
550 divided by 4. Let's do that division. 4 goes into 550 how many times? 4 × 137 is 548, so 550 minus 548 is 2. So, 550/4 is 137 with a remainder of 2, which is 137 2/4. But 2/4 simplifies to 1/2, so 137 1/2.
</execution_1.1>
</Execution_1>

<Final_answer>
Therefore, the car would travel $\boxed{137\frac{1}{2}\text{ miles}}$ in $2\frac{3}{4}$ hours at this speed.
</Final_answer>
</think>