Question

Norton can mow a large lawn in about 4 hours. When Norton and Jesse work together, they can mow the lawn in about 2.5 hours. Jesse wants to know how long it would take her to mow the lawn by herself.

Answer 1

Let x be the time in which Jesse can mow the lawn, this means that in one hour she mows:

`(1)/(x)`

of the lawn in one hour

Now, we know that Norton mows tha lawn in 4 hours, that means that he mows

`(1)/(4)`

of the lawn in one hour.

Now, since when they work together they spent 2.5 hours this means that:

`(1)/(x)+(1)/(4)=(1)/(2.5)`

Now, solving for x we have:

`\begin{gathered} (1)/(x)+(1)/(4)=(1)/(2.5) \\ (4+x)/(4x)=(1)/(2.5) \\ x+4=(4x)/((25)/(10)) \\ x+4=(40)/(25)x \\ x+4=(8)/(5)x \\ (8)/(5)x-x=4 \\ (3)/(5)x=4 \\ x=(4)/((3)/(5)) \\ x=(20)/(3) \end{gathered}`

Therefore Jesse mows the lawn in 20/3 hours (this is, rounded to the hundreths, 6.67 hours.)