students are collecting canned goods for a local food pantry. last year, 12 students were able to distribute…

students are collecting canned goods for a local food pantry. last year, 12 students were able to distribute 1000 flyers in nine hours. this year there are 15 students handing out the same number of flyers. if the time it takes to distribute the flyers varies inversely with the number of students, how long should it take them? ? hours

students are collecting canned goods for a local food pantry. last year, 12 students were able to distribute 1000 flyers in nine hours. this year there are 15 students handing out the same number of flyers. if the time it takes to distribute the flyers varies inversely with the number of students, how long should it take them? ? hours

Answer

Explanation:

Step1: Set up inverse - variation equation

Let $t$ be the time and $n$ be the number of students. Since $t$ varies inversely with $n$, we have $t_1n_1=t_2n_2$.

Step2: Identify values from the problem

Last year, $t_1 = 9$ hours and $n_1=12$ students. This year, $n_2 = 15$ students and we want to find $t_2$.

Step3: Substitute values into the equation

$9\times12=t_2\times15$.

Step4: Solve for $t_2$

$t_2=\frac{9\times12}{15}=\frac{108}{15} = 7.2$.

Answer:

$7.2$