Bethany can mow her family’s lawn in 4 hours. Her brother Colin can mow the lawn in 3 hours. Which equation can be used to find x, the amount of time it would take for Bethany and Colin to mow the lawn together?.
Answer:
The required equation is \(\frac{1}{4}+\frac{1}{3}=\frac{1}{x}\)
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 \(\frac{1}{4}\) lawns per hour.
Her brother Colin can mow the lawn in 3 hours.
i.e.The rate of Colin is \(\frac{1}{3}\) lawns per hour.
Together they work x hours.
i.e. The together rate is \(\frac{1}{x}\) lawns per hour.
So, The equation form according to question is
\(\frac{1}{4}+\frac{1}{3}=\frac{1}{x}\)
Therefore, The required equation is \(\frac{1}{4}+\frac{1}{3}=\frac{1}{x}\)
Solving for x,
\(\frac{3+4}{4\times 3}=\frac{1}{x}\)
\(\frac{7}{12}=\frac{1}{x}\)
\(x=\frac{12}{7}\)
\(x=1.71\)
The amount of time it would take for Bethany and Colin to mow the lawn together is approx 1.71 hours.