Question

linear inequality word problems: medium
the zamboni is an ice resurfacer invented by frank zamboni in the year 1949 to clean and resurface the ice in skating rinks. a zamboni takes 20 minutes to resurface an olympic - sized skating rink. what is the minimum number of zambonis working together at the same rate that could resurface an olympic - sized skating rink in 5 minutes or less?
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Explanation:

Step1: Determine work - rate of one Zamboni

One Zamboni takes 20 minutes to resurface the rink. So the work - rate of one Zamboni is $\frac{1}{20}$ of the rink per minute.

Step2: Let the number of Zambonis be $n$

The combined work - rate of $n$ Zambonis is $\frac{n}{20}$ of the rink per minute.

Step3: Set up an inequality based on time

We want to resurface the rink in 5 minutes or less. The work done in 5 minutes by $n$ Zambonis should be at least 1 (the whole rink). So, $\frac{n}{20}\times5\geq1$.

Step4: Solve the inequality

Simplify the left - hand side of the inequality: $\frac{5n}{20}\geq1$, which simplifies to $\frac{n}{4}\geq1$. Multiply both sides by 4 to get $n\geq4$.

Answer:

4