(100 POINTS AND BRAINLIEST)
Jenna works in an ice cream shop. When she starts her shift the tub of chocolate ice cream is 2/3 full. When she finishes her shift 6 1/2 h later, there is only 1/6 of the tub left. What was the average hourly change in tub fullness?

IMMEDIATE PLEASE.

Answer:

[tex]-1/13\text{ tub per hour}[/tex]

Step-by-step explanation:

First, let's find how much of the tub was used within the time.

We know that the tub was 2/3 full was Jenna started.

And it was only 1/6 full when Jenna ended.

Therefore, to find the amount used, we can subtract 1/6 from 2/3. So:

[tex]u=\frac{2}{3}-\frac{1}{6}[/tex]

Make a common denominator. Change 2/3 to 4/6 by multiplying both layers by 2. So:

[tex]u=\frac{4}{6}-\frac{1}{6}[/tex]

Subtract and reduce:

[tex]u=\frac{3}{6}=\frac{1}{2}[/tex]

Therefore, 1/2 of the tub was used after 6 1/2 hours.

To find the average hourly change, we will put the amount used over the amount of hours. 6 and 1/2 hours is the same as 13/2 hours. Therefore, the hourly change will be:

[tex]c=\frac{\frac{1}{2}}{\frac{13}{2}}[/tex]

Remember when dividing fractions, we:

1) Flip the divisor (the second number).

2) Change the division sign to a multiplication sign.

3) Multiply.

So:

[tex]c=\frac{1}{2}\div\frac{13}{2}\\\Rightarrow c=\frac{1}{2}\times \frac{2}{13}[/tex]

Multiply straight across and reduce:

[tex]c=\frac{2}{26}=\frac{1}{13}[/tex]

However, since we are using up the tub, our rate will be negative. Therefore:

[tex]c=-\frac{1}{13}[/tex]

Therefore, the average hourly rate was -1/13 tub per hour.

This means that after each hour, 1/13 of the tub will be used up.

Edit: Corrected Wrong Answer

Answer: -1/13 of a tub per hour

Step 1: Subtract.

2/3 - 1/6 = ?

Step 2: Find the common denominator.

4/6 - 1/6 = 3/6.

Step 3: Simplify the fraction.

3/6 = 1/2

Step 4: Put 1/2 over 13/2.

1/2 over 13/2

Step 5: Flip divisor around. Then divide.

1/2 ÷ 13/2

Step 6: Multiply.

1/2 × 2/13 = 2/26.

2/26 reduced = 1/13.

Since it was used, now it is -1/13

Answer = -1/13 of a tub per hour

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