Question

complete the parts below. write your answers as whole numbers or fractions in simplest form.
(a) it takes susan 8 weeks to use 2 liters of gasoline in her tractor. give two different unit rates using this relationship.
one unit rate:
(square) (\boldsymbol{\text{select}}) per (\boldsymbol{\text{select}})
another unit rate:
(square) (\boldsymbol{\text{select}}) per (\boldsymbol{\text{select}})
(b) assume she uses the same amount of gasoline each week. how many weeks does it take to use 5 liters of gasoline?
(square) weeks

Explanation:

Part (a)

First Unit Rate (Weeks per Liter)

Step1: Define the rate

We want weeks per liter. So we take the number of weeks (8) divided by the number of liters (2).
$\frac{8}{2} = 4$
So the unit rate is 4 weeks per 1 liter.

Second Unit Rate (Liters per Week)

Step2: Define the rate

We want liters per week. So we take the number of liters (2) divided by the number of weeks (8).
$\frac{2}{8}=\frac{1}{4}$
So the unit rate is $\frac{1}{4}$ liters per 1 week.

Part (b)

Step1: Find the weekly usage rate

From part (a), we know that the rate of gasoline usage (liters per week) is $\frac{1}{4}$ liters per week. Alternatively, we can think of it as for every 8 weeks, 2 liters are used, so per week it's $\frac{2}{8}=\frac{1}{4}$ liters per week.

Step2: Calculate time for 5 liters

We can use the weeks per liter rate. From part (a), we know it's 4 weeks per liter. So for 5 liters, we multiply the rate by the number of liters.
$4\times5 = 20$
Or using the liters per week rate: If she uses $\frac{1}{4}$ liter per week, then to use 5 liters, the time $t$ is given by $t=\frac{5}{\frac{1}{4}}=5\times4 = 20$ weeks.

Answer:

s:
(a) One unit rate: 4 weeks per 1 liter; Another unit rate: $\frac{1}{4}$ liters per 1 week.
(b) $\boxed{20}$ weeks.