# Question #f19cb

Dec 12, 2017

The time it would take for Jack and Marilyn to mow the lawn​ together will be $2$hours and $55$ minutes.

#### Explanation:

Jack mows the lawn in $5$ hours.

That means Jack mows $\frac{1}{5}$ th of the lawn in $1$ hour.

Similarly,

Marilyn can mow the same lawn in $7$hours.

That means, Marilyn mows $\frac{1}{7}$ th of the lawn in $1$ hour.

So if they work together,

In 1 hour they will mow $\frac{1}{5} + \frac{1}{7}$ th of the lawn, i.e.:

$= \frac{1}{5} \left(\frac{7}{7}\right) + \frac{1}{7} \left(\frac{5}{5}\right)$

$= \frac{7}{35} + \frac{5}{35} = \frac{12}{35}$th of the lawn is mowed in $1$ hour.

That means, they will need $\frac{35}{12}$ hours to mow the lawn together,i.e.:

$\frac{35}{12} = 2 \frac{11}{12}$ hours.

$\frac{11}{12}$th of an hour =$\frac{11}{12} x 60$ minutes= $55$ minutes.

The time it would take for Jack and Marilyn to mow the lawn​ together will be $2$hours and $55$ minutes.

Dec 12, 2017

$2 h r s$ $55 \min u t e s$

#### Explanation:

In $5$ hrs Jack mows $1$ Lawn
So in $1$ hr Jack mows $\frac{1}{5}$ Lawn

In $7$ hrs Marilyn mows $1$ Lawn
So in $1$ hr Marilyn mows $\frac{1}{7}$ Lawn

So we can write together Jack and Marilyn in $1$ hr can mow $\frac{1}{5} + \frac{1}{7} = \frac{7 + 5}{35} = \frac{12}{35}$ Lawn

So they can mow a Lawn i.e. $1$ Lawn in $\frac{35}{12} h r s = 2 \frac{11}{12} h r s$=$2 h r s$ $55 \min u t e s$