it takes 8 minutes for byron to fill the kiddie pool in the backyard using only a handheld hose. when his…

it takes 8 minutes for byron to fill the kiddie pool in the backyard using only a handheld hose. when his younger sister is impatient, byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. if the hose and sprinkler are used together, it takes 5 minutes to fill the pool. which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?\no $\frac{5}{8}+5r = 8$\no $\frac{5}{8}+5r = 1$\no $5(\frac{5}{8})=r$\no $\frac{5}{8}=5r$

it takes 8 minutes for byron to fill the kiddie pool in the backyard using only a handheld hose. when his younger sister is impatient, byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. if the hose and sprinkler are used together, it takes 5 minutes to fill the pool. which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?\no $\frac{5}{8}+5r = 8$\no $\frac{5}{8}+5r = 1$\no $5(\frac{5}{8})=r$\no $\frac{5}{8}=5r$

Answer

Answer:

B. $\frac{5}{8}+5r = 1$

Explanation:

Step1: Find hose - filling rate

The hose fills the pool in 8 minutes. So the rate of the hose is $\frac{1}{8}$ of the pool per minute. In 5 minutes, the fraction of the pool filled by the hose is $\frac{1}{8}\times5=\frac{5}{8}$.

Step2: Define sprinkler - filling rate

Let $r$ be the rate of the lawn sprinkler in parts per minute. In 5 minutes, the fraction of the pool filled by the sprinkler is $5r$.

Step3: Set up the equation

When the hose and sprinkler are used together, they fill 1 whole pool in 5 minutes. So the sum of the fraction of the pool filled by the hose and the fraction filled by the sprinkler in 5 minutes is 1. That gives the equation $\frac{5}{8}+5r = 1$.