Answer :
We are given a rate of
[tex]$$3.6 \quad \frac{\text{gal}}{\text{min}}$$[/tex]
and need to convert it to milliliters per second. The conversion factors available are:
- [tex]$$1 \text{ gallon} = 3.79 \text{ liters}$$[/tex]
- [tex]$$1 \text{ liter} = 1000 \text{ milliliters}$$[/tex]
- [tex]$$1 \text{ minute} = 60 \text{ seconds}$$[/tex]
The conversion is set up as follows:
[tex]$$
\frac{3.6 \text{ gal}}{1 \text{ min}} \times \frac{3.79 \text{ L}}{1 \text{ gal}} \times \frac{1000 \text{ mL}}{1 \text{ L}} \times \frac{1 \text{ min}}{60 \text{ sec}} = \text{ ? mL/s}
$$[/tex]
Step 1: Convert gallons to liters
Multiply by the conversion factor [tex]$$\frac{3.79 \text{ L}}{1 \text{ gal}}:$$[/tex]
[tex]$$
3.6 \times 3.79 = 13.644 \quad \frac{\text{L}}{\text{min}}
$$[/tex]
So, [tex]$$3.6 \text{ gal/min} = 13.644 \text{ L/min}.$$[/tex]
Step 2: Convert liters to milliliters
Multiply by the conversion factor [tex]$$\frac{1000 \text{ mL}}{1 \text{ L}}:$$[/tex]
[tex]$$
13.644 \times 1000 = 13644 \quad \frac{\text{mL}}{\text{min}}
$$[/tex]
So, [tex]$$13.644 \text{ L/min} = 13644 \text{ mL/min}.$$[/tex]
Step 3: Convert minutes to seconds
Divide by the conversion factor [tex]$$60 \text{ sec/min}:$$[/tex]
[tex]$$
\frac{13644}{60} \approx 227.4 \quad \frac{\text{mL}}{\text{sec}}
$$[/tex]
So, [tex]$$13644 \text{ mL/min} = 227.4 \text{ mL/sec}.$$[/tex]
Thus, the final conversion is:
[tex]$$
3.6 \frac{\text{gal}}{\text{min}} = 227.4 \frac{\text{mL}}{\text{sec}}
$$[/tex]
To fill in the original tiles:
- The blank for liters per gallon is filled with [tex]$$3.79$$[/tex].
- The blank for the liters in the milliliters conversion is filled with [tex]$$1$$[/tex].
- The blank for seconds in a minute is filled with [tex]$$60$$[/tex].
- The final result is [tex]$$227.4 \frac{\text{mL}}{\text{sec}}.$$[/tex]
[tex]$$3.6 \quad \frac{\text{gal}}{\text{min}}$$[/tex]
and need to convert it to milliliters per second. The conversion factors available are:
- [tex]$$1 \text{ gallon} = 3.79 \text{ liters}$$[/tex]
- [tex]$$1 \text{ liter} = 1000 \text{ milliliters}$$[/tex]
- [tex]$$1 \text{ minute} = 60 \text{ seconds}$$[/tex]
The conversion is set up as follows:
[tex]$$
\frac{3.6 \text{ gal}}{1 \text{ min}} \times \frac{3.79 \text{ L}}{1 \text{ gal}} \times \frac{1000 \text{ mL}}{1 \text{ L}} \times \frac{1 \text{ min}}{60 \text{ sec}} = \text{ ? mL/s}
$$[/tex]
Step 1: Convert gallons to liters
Multiply by the conversion factor [tex]$$\frac{3.79 \text{ L}}{1 \text{ gal}}:$$[/tex]
[tex]$$
3.6 \times 3.79 = 13.644 \quad \frac{\text{L}}{\text{min}}
$$[/tex]
So, [tex]$$3.6 \text{ gal/min} = 13.644 \text{ L/min}.$$[/tex]
Step 2: Convert liters to milliliters
Multiply by the conversion factor [tex]$$\frac{1000 \text{ mL}}{1 \text{ L}}:$$[/tex]
[tex]$$
13.644 \times 1000 = 13644 \quad \frac{\text{mL}}{\text{min}}
$$[/tex]
So, [tex]$$13.644 \text{ L/min} = 13644 \text{ mL/min}.$$[/tex]
Step 3: Convert minutes to seconds
Divide by the conversion factor [tex]$$60 \text{ sec/min}:$$[/tex]
[tex]$$
\frac{13644}{60} \approx 227.4 \quad \frac{\text{mL}}{\text{sec}}
$$[/tex]
So, [tex]$$13644 \text{ mL/min} = 227.4 \text{ mL/sec}.$$[/tex]
Thus, the final conversion is:
[tex]$$
3.6 \frac{\text{gal}}{\text{min}} = 227.4 \frac{\text{mL}}{\text{sec}}
$$[/tex]
To fill in the original tiles:
- The blank for liters per gallon is filled with [tex]$$3.79$$[/tex].
- The blank for the liters in the milliliters conversion is filled with [tex]$$1$$[/tex].
- The blank for seconds in a minute is filled with [tex]$$60$$[/tex].
- The final result is [tex]$$227.4 \frac{\text{mL}}{\text{sec}}.$$[/tex]
