Question: Question 10:
An engine uses 6 gallons of gasoline when it runs for 7 1/2 hours. If it runs at the same speed, how many gallons will be used in 10 hours?
1. **State the problem:**
We need to find how many gallons of gasoline an engine will use in 10 hours if it uses 6 gallons in 7 1\/2 hours and runs at the same speed.
2. **Identify the formula:**
Since the engine uses gasoline at a constant rate, we use the formula for unit rate:
$$\text{Rate} = \frac{\text{Gallons used}}{\text{Time in hours}}$$
3. **Calculate the rate:**
First, convert 7 1\/2 hours to an improper fraction or decimal:
$$7 \frac{1}{2} = 7.5 \text{ hours}$$
Calculate the rate:
$$\text{Rate} = \frac{6}{7.5}$$
4. **Simplify the rate:**
$$\frac{6}{7.5} = \frac{6}{\cancel{7.5}} \times \frac{\cancel{2}}{2} = \frac{12}{15}$$
Now simplify \(\frac{12}{15}\):
$$\frac{12}{15} = \frac{\cancel{12}}{\cancel{15}} = \frac{4}{5} = 0.8 \text{ gallons per hour}$$
5. **Calculate gallons used in 10 hours:**
Use the rate to find gallons for 10 hours:
$$\text{Gallons} = \text{Rate} \times \text{Time} = 0.8 \times 10 = 8$$
6. **Final answer:**
The engine will use **8 gallons** of gasoline in 10 hours.