Jacob with his mower can mow and trim Mr. Clark's yard in 2 x 1/2 hours, while Nicole with her mower can mow and trim the same yard in just 2 hours. If they work together on this yard and keep out of each other's way, in how many minutes can they complete the yard?

Question

anonymous · Answer

Can anybody please explain how to solve this?

anonymous · Answer

1 hour and 7 minutes

anonymous · Answer

can you please explain?

jdoe0001 · Answer

1 hour 6 minutes 46 seconds to be exact :P

jdoe0001 · Answer

jacob takes 2 hours and a half, that is 150mins
nicole takes 2 hours only, that is 120mins

how much does jacob do in 1 hr? that is in 60 secs?

so what's 60secs of 150?  60/150 = 2/5

so jacob in 1 hr has done only 2/5 of the yardwork


what about nicole?  how much has she done in 1 hr?
well, 60/120  = 1/2
so she's really done half the yard in 1hr


how will they fare together?  add their rate

2/5 + 1/2   and use the ratio of 1 hr over the total length of time, that is 
$\bf \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{1}{\textit{total time both will take}}$

jdoe0001 · Answer

then just solve for "total time both will take"

mathstudent55 · Answer

They will work together for x time.
If Jacob can do the job in 2.5 hours, he does x/2.5 of the job.
If Nicole can do the job in 2 hours, she does x/2 of the job.
x is the same for both because when they work together, they work the same amount of time.
Adding their work together, they do the entire job, 1.

$\dfrac{1}{2.5}x + \dfrac{1}{2}x = 1 $

x = 1.1111... hours
The time is $66 \dfrac{2}{3} $ minutes.

anonymous · Answer

thanks a lot:)!