Question

lesson 2 session 2
solving problems with unit rates for ratios with two fractions
read and solve the problems.
1 jaylen’s beta fish tank holds 4\\(\frac{1}{2}\\) gallons of water. it takes him 1\\(\frac{7}{8}\\) minutes to fill it. what is the flow rate of the water in gallons per minute? show your work.

2 bruce walks \\(\frac{3}{4}\\) mile in \\(\frac{1}{5}\\) hour. what is his speed in miles per hour? show your work.

3 kayla mixes \\(\frac{1}{6}\\) pound of salt with \\(\frac{1}{8}\\) bucket of water to make a saline solution. how much salt does she need to use for a full bucket of water? show your work.

Explanation:

Problem 1:

Step1: Recall flow rate formula

Flow rate = Volume / Time. Here, volume is $4\frac{1}{2}$ gallons, time is $1\frac{7}{8}$ minutes. Convert mixed numbers to improper fractions: $4\frac{1}{2}=\frac{9}{2}$, $1\frac{7}{8}=\frac{15}{8}$.

Step2: Divide volume by time

Flow rate = $\frac{9}{2} \div \frac{15}{8} = \frac{9}{2} \times \frac{8}{15}$. Simplify: $\frac{9\times8}{2\times15}=\frac{72}{30}=\frac{12}{5}=2\frac{2}{5}$.

Step1: Recall speed formula

Speed = Distance / Time. Distance is $\frac{3}{4}$ mile, time is $\frac{1}{5}$ hour.

Step2: Divide distance by time

Speed = $\frac{3}{4} \div \frac{1}{5} = \frac{3}{4} \times 5 = \frac{15}{4}=3\frac{3}{4}$.

Step1: Set up proportion

Let $x$ be salt for 1 bucket. Proportion: $\frac{\frac{1}{6}\text{ lb}}{\frac{1}{8}\text{ bucket}}=\frac{x\text{ lb}}{1\text{ bucket}}$.

Step2: Solve for x

Cross - multiply: $x = \frac{1}{6} \div \frac{1}{8}=\frac{1}{6}\times8=\frac{4}{3}=1\frac{1}{3}$.

Answer:

$2\frac{2}{5}$ gallons per minute

Problem 2: