Question

The level of tea h in a tank is 7 ft. It decreases every hour by 4 inches. Which of the following represents the level of tea h depending on the number of hours t?

h=84+4t

h=7-4t

h=84-4t

h=7+4t

Answer 1

To represent the level of tea \( h \) in the tank in relation to the number of hours \( t \), we start with the initial level of tea, which is 7 ft. Since the level decreases by 4 inches every hour, we need to convert 4 inches to feet. There are 12 inches in a foot, so:

\[
4 \text{ inches} = \frac{4}{12} \text{ feet} = \frac{1}{3} \text{ feet}
\]

Thus, the level of tea decreases by \( \frac{1}{3} \) feet for every hour \( t \).

Now, if \( h \) is the level of tea after \( t \) hours, the equation can be expressed as:

\[
h = 7 - \frac{1}{3} t
\]

However, since none of the options given involve fractions, let's find a different expression based on \( t \) in hours with respect to inches. The rate of decrease in inches is given, so we can rethink the expression with the decrease represented in inches:

Starting level of tea: 7 ft = 84 inches (since \( 1 \text{ ft} = 12 \text{ inches} \))

The decrease per hour is 4 inches, so after \( t \) hours, the level in inches is:

\[
h = 84 - 4t
\]

Now, looking through the options provided:

1. \( h = 84 + 4t \)
2. \( h = 7 - 4t \)
3. \( h = 84 - 4t \)
4. \( h = 7 + 4t \)

The correct expression that represents the level of tea \( h \) in relation to the number of hours \( t \) is:

\[
\text{h = 84 - 4t}
\]

So, the answer is: **h = 84 - 4t**.