A cleaning session for a pool in a gym lasts for 35 minutes on weekdays and 45 minutes on weekends. Suppose the time it took to clean the pool was five hours altogether. Write an equation to represent this information and then solve it to determine how many weekday cleaning sessions there were.
As there are two days on the weekend, Saturday and Sunday, we know that the total cleaning time on the weekend will be 45 plus 45. As it takes 35 minutes to clean the pool on weekdays, we know that the total time will be 35𝑥, 35 minutes multiplied by the number of weekdays that the pool is cleaned. The total time was five hours. As there are 60 minutes in an hour and five multiplied by 60 is equal to 300, our equation will be equal to 300.
We’re therefore left with an equation 45 plus 45 plus 35𝑥 is equal to 300. In order to solve this equation, we can firstly add 45 and 45. This gives us 90. Therefore, our equation is now 90 plus 35𝑥 equals 300. Subtracting 90 from both sides of the equation gives us 35𝑥 is equal to 210. And finally, dividing both sides of this equation by 35 gives us 𝑥 equals six. This means that there were six weekday cleaning sessions. Six multiplied by 35 plus two multiplied by 45 is equal to 300 minutes, or five hours.