AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
The Zamboni is an ice resurfacer invented by Frank Zamboni in the year to clean and resurface the ice in skating rinks. A Zamboni takes 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 minutes or less?
Full solution
Q. The Zamboni is an ice resurfacer invented by Frank Zamboni in the year to clean and resurface the ice in skating rinks. A Zamboni takes 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 minutes or less?
- Find Minimum Zambonis: We need to find the minimum number of Zambonis.
- Time Taken by Zamboni: Let the time taken by one Zamboni be minutes.
- Calculate Number of Zambonis: We know minutes.
- Check Time Requirement: We need to resurface the rink in minutes or less.
- Define Number of Zambonis: Let be the number of Zambonis.
- Calculate Total Time: Each Zamboni takes minutes, so Zambonis will take rac{10}{n} minutes.
- Inequality Simplification: We need .
- Divide by : Simplify:
- Determine Minimum Zambonis: Divide both sides by : rac{1}{n} \leq \ rac{1}{1}
- Determine Minimum Zambonis: Divide both sides by : rac{1}{n} \leq 1 Since rac{1}{n} must be less than or equal to , must be greater than or equal to .
- Determine Minimum Zambonis: Divide both sides by : rac{1}{n} \leq \ 1 Since rac{1}{n} must be less than or equal to , must be greater than or equal to . The minimum number of Zambonis is .
