Math  /  Algebra

Question20. People are entering a stadium at a steady rate of 32 people per minute. When the gates open, there are already 46 people in the stadium. No one leaves the stadium for the first hour after the gates have opened. (a) How many people will be in the stadium 30 minutes after it opens? Show the calculations that lead to you answer. (b) Write a linear equation for the number of people, nn, as a function of the time in minutes, mm, since the gates were opened. 32(30)=960 people +46 people 1006 people \begin{aligned} 32(30) & =960 \text { people } \\ & +46 \text { people } \\ & 1006 \text { people } \end{aligned} n(m)=32n+46n(m)=32 n+46 (c) After one hour, no additional people enter, but some start to leave. If it takes a total of 4 hours for the stadium to completely empty, what is the average rate at which people leave, in people per hour? Show the calculations that lead to your answer. h(60)=32(60)+46=1966 prople \begin{aligned} h(60) & =32(60)+46 \\ & =1966 \text { prople } \end{aligned} =1966=1966 people 19663=6553 people pe \frac{1966}{3}=6553 \geqslant \text { people pe }

Studdy Solution
(a) There will be **1006** people in the stadium after 30 minutes. (b) The equation is n(m)=32m+46n(m) = 32m + 46. (c) The average rate at which people leave is approximately **655 people per hour**.

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