Question

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 1

In 4 hours Bethany did the whole fraction 1 of the house.

In 1 hour he would do 1/4 of it.

In 3 hours Colin did the whole fraction 1 of the house.

In 1 hour he would do 1/3 of it.

In 1 hour they would both do (1/4 + 1/3)

If it takes both of them x hours to finish 1 whole fraction of the house.

In 1 hour they will both do 1/x

That means that:

1/x = 1/4 + 1/3

That is the equation. x can be solved for.

Answer 2

The equation is
`x=(12)/(7)`

Explanation:

The amount of time it would take for Bethany and Colin to mow the lawn together = x

Bethany can mow her family’s lawn in 4 hours.

Let the mow work be m.

`\texttt{Rate of Bethany}=(m)/(4)`

Colin can mow the lawn in 3 hour

`\texttt{Rate of Colin}=(m)/(3)`

Time required when they mow together

`x=(m)/((m)/(4)+(m)/(3))=(12)/(7)\\\\x=(12)/(7)`

The equation is
`x=(12)/(7)`