Respuesta :
now, a whole, will be 15/15 or 1 whole.
now, the sprinkler does 1/15 of the lawn in 1/3 of an hour, how long will it be to do the whole 15/15?
[tex]\bf \begin{array}{ccll} lawn&hours\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{15}&\frac{1}{3}\\\\ \frac{15}{15}&h \end{array}\implies \cfrac{\quad \frac{1}{15}\quad }{\frac{15}{15}}=\cfrac{\quad \frac{1}{3}\quad }{h}\implies \cfrac{1}{15}\cdot \cfrac{15}{15}=\cfrac{\quad \frac{1}{3}\quad }{\frac{h}{1}} \\\\\\ \cfrac{1}{15}=\cfrac{1}{3}\cdot \cfrac{1}{h}\implies \cfrac{1}{15}=\cfrac{1}{3h}\implies 3h=15\implies h=\cfrac{15}{3}\implies h=5[/tex]
now, the sprinkler does 1/15 of the lawn in 1/3 of an hour, how long will it be to do the whole 15/15?
[tex]\bf \begin{array}{ccll} lawn&hours\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{15}&\frac{1}{3}\\\\ \frac{15}{15}&h \end{array}\implies \cfrac{\quad \frac{1}{15}\quad }{\frac{15}{15}}=\cfrac{\quad \frac{1}{3}\quad }{h}\implies \cfrac{1}{15}\cdot \cfrac{15}{15}=\cfrac{\quad \frac{1}{3}\quad }{\frac{h}{1}} \\\\\\ \cfrac{1}{15}=\cfrac{1}{3}\cdot \cfrac{1}{h}\implies \cfrac{1}{15}=\cfrac{1}{3h}\implies 3h=15\implies h=\cfrac{15}{3}\implies h=5[/tex]
The amount of time will it take to water the entire lawn will be 45 hours.
What are ratios and proportions?
The ratio is the two numbers that are divided from one to another.
The ratio could be positive negative or zero.
The denominator of any ratio should not be zero.
Given that sprinklers fill lawns 1/15 portion in 1/3 hour time
1/15 portion of lawn ⇒ 1/3 hours of time
1 portion(a complete portion of lawn) = 15 hours hence, the sprinkler feeds the entire lawn for 15 hours.
For more information about ratio and proportion
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