Let's solve the problem step by step:

Part (a)

Keith uses 2 liters of gasoline in 14 weeks. We need to find two different unit rates to represent this relationship.

1. Unit Rate of Gasoline per Week:

   • Since he uses 2 liters in 14 weeks, the amount of gasoline he uses per week is: $\frac{2 \text{ liters}}{14 \text{ weeks}} = \frac{1}{7} \text{ liters per week}$

2. Unit Rate of Weeks per Liter:

   • Alternatively, we can find the number of weeks it takes him to use 1 liter of gasoline: $\frac{14 \text{ weeks}}{2 \text{ liters}} = 7 \text{ weeks per liter}$

So, the two unit rates are:

• $\frac{1}{7}$ liters per week
• 7 weeks per liter

Part (b)

We need to calculate how many weeks it will take him to use 5 liters of gasoline, assuming he uses the same amount each week.

From our second unit rate, we know he takes 7 weeks to use 1 liter of gasoline. Therefore, for 5 liters, it will take: $5 \times 7 = 35 \text{ weeks}$

Summary of Answers

• (a) The two unit rates are:
  1. $\frac{1}{7}$ liters per week
  2. 7 weeks per liter
• (b) It takes 35 weeks to use 5 liters of gasoline.

Would you like more details on any part of this solution?

Here are some related questions for further exploration:

1. If Keith increased his gasoline usage to 4 liters over 14 weeks, what would the new unit rates be?
2. How many liters of gasoline would he use in 21 weeks at the current rate?
3. What if he wanted to use 10 liters of gasoline? How many weeks would that take?
4. How would the answer change if he used 3 liters in 14 weeks?
5. What would the unit rates be if Keith used 2 liters over a period of 10 weeks instead?

Tip: When converting between unit rates, make sure to clearly set up your ratios to maintain accuracy.