# Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 3 hours. How much time would it take for them to mow the lawn together?

Mar 30, 2017

$\frac{12}{7}$ hours

#### Explanation:

Since Jack takes $4$ hours. to mow his lawn, he mows $\frac{1}{4}$ of his lawn each hour. Since Marilyn takes $3$ hours., he mows $\frac{1}{3}$ of the same lawn each hour.

Suppose that they spend $t$ hours working together mowing the lawn. Jack can get $\frac{t}{4}$ of his lawn done, and Marilyn can get $\frac{t}{3}$ of his lawn done. In total, $\frac{t}{4} + \frac{t}{3}$ is done.

When they finish, exactly $1$ of the lawn is done. In other words, $\frac{t}{4} + \frac{t}{3} = 1$. We combine the left-hand side into one fraction: $\frac{7 t}{12} = 1$. Solving for $t$, we get $t = \frac{12}{7}$ hours.

Mar 30, 2017

Jack and Marilyn together will take $1 \frac{5}{7}$ hour to mow the lawn.

#### Explanation:

Jack mows his lawn in $4$ hours.
So in $1$ hour Jack mows $\frac{1}{4}$th of his lawn.

Marilyn mows same lawn in $3$ hours.
So in $1$ hour Marylin mows $\frac{1}{3}$rd of the lawn.

So in $1$ hour both together will mow $\frac{1}{4} + \frac{1}{3} = \frac{7}{12}$ part of the lawn.
Therefore, they both together will take $\frac{1}{\frac{7}{12}} = \frac{12}{7} = 1 \frac{5}{7}$ hour to mow the lawn. [Ans]