MATH SOLVE

3 months ago

Q:
# If a sprinkler waters 1 over 15 of a lawn in 1 over 3 hour, how much time will it take to water the entire lawn? 5 hours 15 hours 18 hours 45 hours

Accepted Solution

A:

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]