Question

A garden hose fills a 4-gallons bucket in 20 seconds. The number of gallons, y, is proportional to thw number of seconds, x, that the water is running. Write two equations showing the relationship between y and x; one where k is a fraction and one where k is a decimal.

Answer 1

The number of gallons, y, is proportional to thw number of seconds, x, that the water is running, therefore:

`\begin{gathered} y=kx \\ \text{where:} \\ k=\text{constant of proportionality} \end{gathered}`

A garden hose fills a 4-gallons bucket in 20 seconds, so:

`\begin{gathered} 4=k\cdot20 \\ \text{solve for k:} \\ k=(4)/(20)=(1)/(5)=0.2 \end{gathered}`

Hence:

`\begin{gathered} y=(1)/(5)x \\ or \\ y=0.2x \end{gathered}`