Pira drives 825 miles to California. The trip takes him 17 hours. He uses 38 gallons of gas on the trip, which costs him $125.

Question

Find his speed.

Find his gas mileage

Find the unit price he paid for gas

Answer 1

To find Pira's speed, gas mileage, and the unit price he paid for gas, we can break it down as follows:

1. Finding Speed

Speed is calculated using the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Where:

• Distance = 825 miles
• Time = 17 hours

Calculating the speed: \[ \text{Speed} = \frac{825 \text{ miles}}{17 \text{ hours}} \approx 48.24 \text{ miles per hour} \]

2. Finding Gas Mileage

Gas mileage (miles per gallon) is calculated using the formula: \[ \text{Gas Mileage} = \frac{\text{Distance}}{\text{Gallons of gas}} \] Where:

• Distance = 825 miles
• Gallons of gas = 38 gallons

Calculating the gas mileage: \[ \text{Gas Mileage} = \frac{825 \text{ miles}}{38 \text{ gallons}} \approx 21.71 \text{ miles per gallon} \]

3. Finding Unit Price Paid for Gas

The unit price of gas is calculated using the formula: \[ \text{Unit Price} = \frac{\text{Total Cost}}{\text{Gallons of gas}} \] Where:

• Total Cost = $125
• Gallons of gas = 38 gallons

Calculating the unit price: \[ \text{Unit Price} = \frac{125 \text{ dollars}}{38 \text{ gallons}} \approx 3.29 \text{ dollars per gallon} \]

Summary of Results:

• Speed: 48.24 miles per hour
• Gas Mileage: 21.71 miles per gallon
• Unit Price of Gas: $3.29 per gallon

Answer 2

Caleb drives for 3 hours at 15 miles per hour. How far does he travel?

What is the unit rate?

Answer 3

To find out how far Caleb travels, we can use the formula for distance:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Where:

• Speed = 15 miles per hour
• Time = 3 hours

Calculating the distance:

\[ \text{Distance} = 15 \text{ miles/hour} \times 3 \text{ hours} = 45 \text{ miles} \]

Unit Rate

The unit rate in this context refers to Caleb's speed, which is the distance he travels per hour. Since his speed is already given as 15 miles per hour, the unit rate is:

\[ \text{Unit Rate} = 15 \text{ miles per hour} \]

Summary of Results:

• Distance traveled: 45 miles
• Unit Rate (Speed): 15 miles per hour

Answer 4

Choose the better buy. $12.95 for 3 pounds of nuts or $21.45 for 5 pounds of nuts.
Express and compare the unit rates.

Answer 5

To determine the better buy, we need to calculate the unit rates for each option. The unit rate can be found by dividing the total cost by the number of pounds.

Option 1: $12.95 for 3 pounds of nuts

\[ \text{Unit Rate (Option 1)} = \frac{\text{Total Cost}}{\text{Pounds}} = \frac{12.95}{3} \approx 4.32 \text{ dollars per pound} \]

Option 2: $21.45 for 5 pounds of nuts

\[ \text{Unit Rate (Option 2)} = \frac{\text{Total Cost}}{\text{Pounds}} = \frac{21.45}{5} \approx 4.29 \text{ dollars per pound} \]

Comparison of Unit Rates

• Option 1: approximately $4.32 per pound
• Option 2: approximately $4.29 per pound

Conclusion

Option 2 (5 pounds for $21.45) is the better buy, as it has a lower unit rate of approximately $4.29 per pound compared to $4.32 per pound for Option 1.