Question

a. Jill's bowl of pudding contains 12 ounces, and she eats (1)/(10) of an ounce each second. Barb's bowl of pudding contains (1)/(10) of an ounce, and she adds 2 ounces each second. After how many seconds will the two bowls contain the same amount of pudding?

Answer 1

17/3 seconds

Explanation:

We can model the problem using two linear functions in the slope-intercept form, whose general equation is given by:

y = mx + b, where

• m is the slope,
• and b is the y-intercept.

In the context of the problem:

• The slope is the rate at which the ounces decrease per second.
• The y-intercept is the original amount of ounces in the bowl.
• y is the amount remaining in the bowl.
• x is the seconds that have passed.

For Jill's equation:

• The slope is -1/10, which means her bowl decreases by 1 oz every 10 seconds.
• The y-intercept is 12 as this is the original amount in the bowl.

Jill's equation: y = -1/10x + 12

For Barb's equation:

• The slope is 2 oz and thus her bowl increases by 2 oz every second.
• The y-intercept is 1/10 as this is the original amount in the bowl.

Barby's equation = y = 2x + 1/10

Now we can set the two equations equal to each other to solve for x, the time (in seconds) at which the two bowls will contain the same amount of pudding:

-1/10x + 12 = 2x + 1/10

Subtracting 1/10 from both sides give us:

-1/10x + 119/10 = 2x

Adding -1/10x to both sides gives us:

119/10 = 21/10x

Dividing both sides by 21/10 gives us:

17/3 = x

Thus, the two bowls will contain the same amount after 17/3 of a second (i.e., about 5.67 seconds)