Give step-by-step solution with explanation and final answer:
Please do not include two equal sign in the same line.| | A 47taon crosses th Atari Ocean (3000 mies) wi an speed of 600 mbes par hou. T

Question

Give step-by-step solution with explanation and final answer: 
Please do not include two equal sign in the same line.| | A 47taon crosses th Atari Ocean (3000 mies) wi an speed of 600 mbes par hou. The cost in dlr) pe passangr given by
x
Clg=2000 %+ B00,
Where xs the ground speed (airspeed + wind)
Ea a
(a) Whats the cost per passenger fo quiescent (no wind) conditons?
$[[] Round to the nearest cent as needed)
(6) Whats the cost por passenger with a head wind of 50 miles per hour?
S(T] (Round to the nearest cent as needed)
(c) Wt is the cost per passenger wih a tail wind of 100 miles per hour?
S[] (Round to the nearest cent as needed)
(6) Whats the cost per passenger with a head wind of 100 miles por hour?
5] (Round othe nearest cont as noaded)

VIPSolutions · Accepted Answer

Let's solve each part step by step using the formula:

$$
C(x) = 200 + \frac{x}{15} + \frac{33,000}{x}
$$

where $ x $ is the ground speed (airspeed ± wind speed).

The airspeed is **600 mph**.

---

### (a) Quiescent (no wind) conditions:
- Wind = 0, so $ x = 600 $ mph

Plug into the formula:

$$
C(600) = 200 + \frac{600}{15} + \frac{33,000}{600}
$$

Calculate each term:

$$
\frac{600}{15} = 40
$$
$$
\frac{33,000}{600} = 55
$$
$$
C(600) = 200 + 40 + 55
$$
$$
C(600) = 295
$$

**Final Answer:**  
$\boxed{295.00}$

---

### (b) Head wind of 50 mph:
- Ground speed = 600 - 50 = **550 mph**

$$
C(550) = 200 + \frac{550}{15} + \frac{33,000}{550}
$$

Calculate each term:

$$
\frac{550}{15} \approx 36.67
$$
$$
\frac{33,000}{550} \approx 60.00
$$
$$
C(550) = 200 + 36.67 + 60.00
$$
$$
C(550) \approx 296.67
$$

**Final Answer:**  
$\boxed{296.67}$

---

### (c) Tail wind of 100 mph:
- Ground speed = 600 + 100 = **700 mph**

$$
C(700) = 200 + \frac{700}{15} + \frac{33,000}{700}
$$

Calculate each term:

$$
\frac{700}{15} \approx 46.67
$$
$$
\frac{33,000}{700} \approx 47.14
$$
$$
C(700) = 200 + 46.67 + 47.14
$$
$$
C(700) \approx 293.81
$$

**Final Answer:**  
$\boxed{293.81}$

---

### (d) Head wind of 100 mph:
- Ground speed = 600 - 100 = **500 mph**

$$
C(500) = 200 + \frac{500}{15} + \frac{33,000}{500}
$$

Calculate each term:

$$
\frac{500}{15} \approx 33.33
$$
$$
\frac{33,000}{500} = 66.00
$$
$$
C(500) = 200 + 33.33 + 66.00
$$
$$
C(500) = 299.33
$$

**Final Answer:**  
$\boxed{299.33}$

---

### **Summary Table**

| Condition                 | Ground Speed (x) | Cost per Passenger ($) |
|---------------------------|------------------|------------------------|
| (a) No wind               | 600              | 295.00                 |
| (b) 50 mph head wind      | 550              | 296.67                 |
| (c) 100 mph tail wind     | 700              | 293.81                 |
| (d) 100 mph head wind     | 500              | 299.33                 |

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