Question

organizing information for a work a medium water hose can fill a pool in 30 minutes. a larger water hose can fill the same pool in 20 minutes. if both hoses are turned on at the same time, how long will it take to fill the pool? what equation can be used to solve this work problem? how many minutes will it take both hoses to fill the pool? drag each tile to the correct cell in the table. t \\(\frac{1}{30}\\) \\(\frac{1}{20}\\) \\(\frac{1}{30}t\\) \\(\frac{1}{20}t\\) rate (part/min) medium hose large hose time (min) part of pool filled

Explanation:

Step1: Determine Rates

The medium hose fills the pool in 30 minutes, so its rate is $\frac{1}{30}$ part per minute. The large hose fills it in 20 minutes, so its rate is $\frac{1}{20}$ part per minute.

Step2: Set Up Equation for Time \( t \)

When working together, the sum of their parts filled equals 1 (the whole pool). So the equation is $\frac{1}{30}t + \frac{1}{20}t = 1$.

Step3: Solve the Equation

First, find a common denominator for the fractions, which is 60. Rewrite the equation: $\frac{2}{60}t + \frac{3}{60}t = 1$. Combine like terms: $\frac{5}{60}t = 1$, simplify to $\frac{1}{12}t = 1$. Multiply both sides by 12: \( t = 12 \).

Answer:

The equation is $\frac{1}{30}t + \frac{1}{20}t = 1$ and it takes 12 minutes.