Respuesta :
Answer:
The required equation is [tex]\frac{1}{4}+\frac{1}{3}=\frac{1}{x}[/tex]
The amount of time it would take for Bethany and Colin to mow the lawn together is approx 1.71 hours.
Step-by-step explanation:
Given : Bethany can mow her family’s lawn in 4 hours. Her brother Colin can mow the lawn in 3 hours.
To find : Which equation can be used to find x, the amount of time it would take for Bethany and Colin to mow the lawn together?
Solution :
Let the whole lawn of the house be 1 unit.
Bethany can mow her family’s lawn in 4 hours.
i.e.The rate of Bethany is [tex]\frac{1}{4}[/tex] lawns per hour.
Her brother Colin can mow the lawn in 3 hours.
i.e.The rate of Colin is [tex]\frac{1}{3}[/tex] lawns per hour.
Together they work x hours.
i.e. The together rate is [tex]\frac{1}{x}[/tex] lawns per hour.
So, The equation form according to question is
[tex]\frac{1}{4}+\frac{1}{3}=\frac{1}{x}[/tex]
Therefore, The required equation is [tex]\frac{1}{4}+\frac{1}{3}=\frac{1}{x}[/tex]
Solving for x,
[tex]\frac{3+4}{4\times 3}=\frac{1}{x}[/tex]
[tex]\frac{7}{12}=\frac{1}{x}[/tex]
[tex]x=\frac{12}{7}[/tex]
[tex]x=1.71[/tex]
The amount of time it would take for Bethany and Colin to mow the lawn together is approx 1.71 hours.
