Question

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

Answer 1

`1.71" hours "` to 2 decimal places

`1" hours "42" minutes "51 1/2" seconds "larr` approximately

Explanation:

Let the total count of work effort needed be `W`

Let Jack's rate of work per hour be `w_j`
Let Marilyn's rate of work per hour be `w_m`

Let the unknown time in hours be `t`

`color(blue)("Initial condition")`

`3" hours"xxw_j =W color(white)("d")=> w_j=W/3`

`4" hours"xxw_m=W color(white)("d")=> w_m=W/4`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Working together they achieve "W" amount of work")`

`[txxw_j]+[txxw_m] = W`

Substituting for `w_m and w_j`

`[txxW/3]+[txxW/4]=W`

`(tW)/3+(tW)/4=W`

Divide both sides by `W`

`t/3+t/4=1`

`(4t)/12+(3t)/12=1`

`4t+3t=12`

`t=12/7" hours" =1.714285... ->1.71" hours "` to 2 decimal places

`t= 1" hours "42" minutes "51 1/2" seconds "larr` approximately

color(white)("d")