Let's break down the information in the problem:

• Frank uses 5/12 of a tank of gas to drive to Stan’s Farm and back.
• He uses 1/3 of a tank of gas to drive to Louisa’s Farm and back.
• There is a road between Stan's Farm and Louisa’s Farm that is 120 miles long.
• Frank currently has 5/8 of a tank of gas.

The question asks if Frank can drive from his store to Stan’s Farm, then to Louisa’s Farm, and back to his store, all with 5/8 of a tank of gas, or if he should buy more gas.

Plan:

1. We need to calculate how much gas it takes to make the full round trip: from the store to Stan’s Farm, then to Louisa’s Farm, and back to the store.
2. Compare this total amount with the available 5/8 of a tank.

Step 1: Gas for the trip to Stan’s Farm

• The trip to Stan’s Farm and back takes 5/12 of a tank of gas.

Step 2: Gas for the trip from Stan’s Farm to Louisa’s Farm

• For this, we’ll use the information from the trip to Louisa’s Farm. Driving to Louisa’s Farm and back takes 1/3 of a tank.
• Since Stan’s Farm is on the way, we assume half of the gas for the Louisa trip is used going from Stan's Farm to Louisa's Farm and back. Half of 1/3 is: $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \text{ of a tank}$

Step 3: Total gas for the entire journey

• The trip to Stan’s Farm and back: 5/12 of a tank.
• The trip from Stan’s Farm to Louisa’s Farm and back: 1/6 of a tank.

Adding these together: $\frac{5}{12} + \frac{1}{6}$ Convert both fractions to have the same denominator (12): $\frac{5}{12} + \frac{2}{12} = \frac{7}{12}$

Step 4: Compare to available gas

• Frank has 5/8 of a tank of gas.
• Convert 5/8 to a fraction with denominator 24 to compare: $\frac{5}{8} = \frac{15}{24}$
• Convert 7/12 to the same denominator (24): $\frac{7}{12} = \frac{14}{24}$

Since 15/24 (available gas) is greater than 14/24 (required gas), Frank has enough gas for the trip.

Conclusion:

Yes, Frank can complete the trip with 5/8 of a tank of gas, and he does not need to buy more gas.

Would you like any further clarification? Here are 5 related questions to consider:

1. How would the situation change if the distance between Stan's and Louisa's farms affected gas consumption differently?
2. What would happen if Frank only had 1/2 a tank of gas? Would he make the trip?
3. Can you convert different fractional fuel amounts to decimals to check consistency?
4. How might adding another farm or destination affect his fuel calculations?
5. What if Frank’s vehicle became less fuel-efficient halfway through his journey?

Tip:

When comparing fractions, always ensure they have a common denominator to make addition or comparison easier!