`(40" yd")/(4.5" sec")*(3" ft")/(1" yd")*(5,280" ft")/(1" mi")*(60" sec")/(1" min")*(60" min")/(1" hr")`
A sprinter who can run the 40-yard dach in 4.5 seconds converts his speed into miles per hour, using the product abov. Which fraction in the product is incorrectly written to convert his speed?

Options

A. `(3" ft")/(1 "yd")`
B. `(5,280" ft")/(1" mi")`
C. `(60" sec")/(1" min")`
D. `(60" min")/(1" hr")`

Answer

To solve the problem, we need to analyze the given expression for converting the sprinter's speed from yards per second to miles per hour. The expression is:

\[ \frac{40 \text{ yd}}{4.5 \text{ sec}} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{5,280 \text{ ft}}{1 \text{ mi}} \times \frac{60 \text{ sec}}{1 \text{ min}} \times \frac{60 \text{ min}}{1 \text{ hr}} \]

### Step 1: Identify the units involved
The units we have in the expression are:
- Yards (yd)
- Feet (ft)
- Miles (mi)
- Seconds (sec)
- Minutes (min)
- Hours (hr)

### Step 2: Convert yards to feet
We know that:
1 yard = 3 feet.

So, the conversion from yards to feet is given by:
\[ \frac{3 \text{ ft}}{1 \text{ yd}} \]

### Step 3: Convert feet to miles
We also know that:
1 mile = 5,280 feet.

Thus, the conversion from feet to miles should be:
\[ \frac{1 \text{ mi}}{5,280 \text{ ft}} \]

### Step 4: Convert seconds to hours
We can convert seconds to hours using:
1 hour = 60 minutes and 1 minute = 60 seconds, so:
\[ \frac{60 \text{ sec}}{1 \text{ min}} \times \frac{60 \text{ min}}{1 \text{ hr}} = \frac{3600 \text{ sec}}{1 \text{ hr}} \]

### Step 5: Analyze the given product
Now, let's analyze the given product:
1. The numerator must contain miles and the denominator must contain hours for the final speed to be in miles per hour.
2. The given product has:
- 40 yd in the numerator
- 4.5 sec in the denominator
- 3 ft per 1 yd (which converts yards to feet)
- 5,280 ft per 1 mi (which should be written as 1 mi per 5,280 ft)
- 60 sec per 1 min
- 60 min per 1 hr

### Step 6: Identify the incorrect fraction
The incorrect fraction in the product is:
\[ \frac{5,280 \text{ ft}}{1 \text{ mi}} \]
This should be:
\[ \frac{1 \text{ mi}}{5,280 \text{ ft}} \]

### Conclusion
Thus, the fraction that is incorrectly written to convert the speed is:
\[ \frac{5,280 \text{ ft}}{1 \text{ mi}} \]