Question

17. A tub can drain 24 gallons of water in 5 minutes. What is this rate in cups per second? Use conversion factors to determine the answer. Show your work.

Answer 1

The tub is said to drain 24 gallons of water in 5 minutes.

The rate at which water is drained is;

`\text{Rate r}=(volume)/(time)`

The volume is given as 24 gallons.

Recall that 1 US gallon is equivalent to 16 US cups.

`\begin{gathered} \text{Volume = 24 gallons }*16\text{ cups/gallon} \\ \text{Volume}=384\text{ cups} \end{gathered}`

Time taken is given as 5 minutes.

since the rate is in cups per second, we need the convert the time to seconds;

`\begin{gathered} \text{Time}=5\text{ minutes}*60\text{ seconds/minute} \\ \text{Time}=300\text{ seconds} \end{gathered}`

Using the rate formula, The rate in cups per second is;

`\text{Rate r}=(384)/(300)=1.28\text{ cups/second}`

The rate in cups per second is 1.28 cups per second