I watched 1000 ants build an anthill in 5 hours. Working at the same rate, 2500 ants could have built the anthill in ? hours?
A. 1
B. 2
C. 3
D. 4
I made a proportion of 1000/5=2500/x, and got 12.5, but that's not a choice. HELPS!
None of your answer choices can possibly be correct. The answers are all less than 5 hours, but your question asks about the time for more ants.
I suspect you miscopied the question.
That's what I thought, but that's what the question says... Might be a bad question. Thanks though!
The time is inversely proportional to the number of ants, that is,
as the number of ants increase, the time needed to build the anthill decreases
time = k/ants
if time = 5, ants = 1000
5 = k/1000
k = 5000
time = 5000/ants
time = 5000/2500
time = 2 hrs
or simply as an inverse ratio
time/5 = 1000/2500
time = 5000/2500 = 2
Oops! I really screwed this one up.
Thanks, Reiny.
Welcome Ms Sue, :)
Great job setting up the proportion! To solve this problem, you can use the concept of ratios.
The ratio of ants to time is constant, meaning that if you have twice the number of ants, it would take half the time to complete the task.
In this case, you have 1000 ants completing the anthill in 5 hours. To determine how long it would take 2500 ants to complete the same anthill, you can set up the proportion:
1000 ants / 5 hours = 2500 ants / x hours
To solve for x, you can cross multiply:
1000 * x = 2500 * 5
Now, you can solve for x by dividing both sides of the equation by 1000:
x = (2500 * 5) / 1000
Simplifying further:
x = 12.5
Now, you correctly calculated that it would take 12.5 hours for 2500 ants to complete the anthill. However, you're looking for the available answer choices. Since 12.5 is not among the options, you would choose the closest whole number. In this case, the closest whole number to 12.5 is 12. Therefore, the correct answer would be:
D. 4
I hope this helps! Let me know if you have any further questions.