An earthworm of length 15cm is crawling along at 2cm/s. an ant overtakes the worm in 5 seconds. how fast is the ant walking?

Assume we have a number line, where the tail of the worm is at x=0. This means that the head of the worm is at x=15.

Also, we know that the coordinate of the head of the worm follows this equation:

Where is the time in seconds. In fact, we know that the worm gains 2 centimeters per second.

Now, assume that the ant also starts at x=0, and walks with a certain rate of centimeters per second. This means that the equation for the position of the ant is

Now, we know that after 5 seconds the ant is in the same position as the head of the worm, which means

We know the equation for both expressions, so let's subtitute them in:

So, the ant walks at a rate of 5cm per second.

yes.. it's proven to be 36.

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max.   it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to.   the number combination of adults (x) and campers (y) cannot exceed this 525 max.   therefore:

x + y ≤ 525

now we talk about cost.   it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults.   same with the campers, who cost $5 to feed.   the adults can be represented by 9x and the campers can be represented by 5y.   since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200