Question

An oil tanker empties at $3.5$ gallons per minute. How do you express this rate as cups per seconds, rounded to the nearest tenth?

Answer 1

Hint: For finding the rate as cups per seconds to empty $3.5$ gallons, we will have to find the ratio between cups and gallons. After getting the ratio, we will have to convert time from minutes to seconds. Then we will do the necessary calculation so that we will get the required value to empty the gallons.

Complete step-by-step solution:
Since, we have the value that says an oil tanker can empty $3.5$ gallons in a minute. But now we have to find this value in cups per seconds. So, we will have to find the relation between cups and gallons. As we know that $1$ gallon is equal to $4$ quarts, $1$ quart is equal to $4$ cups. So, we have $1$ gallon is equal to $16$ quarts as:
\[\Rightarrow 1\text{ gallon}=4\text{ quarts}\] … $\left( i \right)$
\[\Rightarrow 1\text{ quart}=4\text{ cups}\] … $\left( ii \right)$
After combining equation $\left( i \right)$ and $\left( ii \right)$, we will have:
\[\Rightarrow 1\text{ gallon}=\left( 4\times \text{4} \right)\text{ cups}\]
Now, we will get the relation between gallon and cups as:
\[\Rightarrow 1\text{ gallon}=16\text{ cups}\] … $\left( iii \right)$
Here, we will change the unit of time also as:
$1\text{ minute}=60\text{ seconds}$ … $\left( iv \right)$
According to question, we have:
$\Rightarrow \dfrac{3.5\text{ gallons}}{1\text{ minute}}$
Now, we will use equation $\left( iii \right)$ and equation $\left( iv \right)$in the above fraction, we will have:
$\Rightarrow \dfrac{3.5\text{ }\times \text{ 16cups}}{1\text{ }\times \text{ 60 seconds}}$
Here, we will apply multiplication in numerator and denominator as:
$\Rightarrow \dfrac{\text{56 cups}}{\text{60 seconds}}$
Now, we will use division method to get the value in simplified manner that would be in decimal number as:
$\Rightarrow 0.9\overline{3}\dfrac{\text{ cups}}{\text{ seconds}}$
Hence, we got the required ratio as $0.9\overline{3}$ cups per seconds and approximately it is 1 cup per second

Note: Since, in the question we have given a ratio in some units and asked to calculate this ratio in different units. So, we need to know the relation between these units so that we can convert one unit in different forms. For example, we know that both kilometer and centimeter is the unit of distance and $1$ kilometer is equal to $1000$ meters and $1$ meter is equal to $100$ centimeters. So, we have the relation as $1$ kilometer is equal to $1,00,000$ centimeters.