SOLUTION: Jack usually mows his lawn in 7 hours. Marilyn can move the same yard in 5 hours. How much time would it take for them to mow the lawn together? They could mow the lawn in ___ h

Algebra ->  Rational-functions -> SOLUTION: Jack usually mows his lawn in 7 hours. Marilyn can move the same yard in 5 hours. How much time would it take for them to mow the lawn together? They could mow the lawn in ___ h      Log On


   

Question 866236: Jack usually mows his lawn in 7 hours. Marilyn can move the same yard in 5 hours. How much time would it take for them to mow the lawn together?
They could mow the lawn in ___ hours if they worked together?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x = time it takes for Jack to do the job alone
y = time it takes for Marilyn to do the job alone
z = time it takes for them to get the job done when they work together. This is assuming that one person doesn't slow the other down and they work in the most efficient way as a team.


When we make those definitions above, it turns out that we can tie x,y,z together with this equation

1%2Fx+%2B+1%2Fy+=+1%2Fz


In this case,


x = 7
y = 5
z = unknown (leave it as z for now)


Plug those into the equation and solve for z


1%2Fx+%2B+1%2Fy+=+1%2Fz


1%2F7+%2B+1%2F5+=+1%2Fz


5%2F35+%2B+1%2F5+=+1%2Fz


5%2F35+%2B+7%2F35+=+1%2Fz


%285+%2B+7%29%2F35+=+1%2Fz


12%2F35+=+1%2Fz


12%2Az+=+35%2A1


12z+=+35


z+=+35%2F12


z+=+35%2F12


So it will take highlight%2835%2F12%29 hours for them to do the job if they work together. This is assuming that one person doesn't slow the other down and they work in the most efficient way as a team.


Since 35%2F12+=+2+%26+11%2F12, this means it takes highlight%282+%26+11%2F12%29 hours (2 hours, 55 minutes)


If you want the time in minutes only, then multiply it by 60 to get %2835%2F12%29%2A60+=+175 minutes


Note: the time it takes, in hours only, as a decimal is approximately 35/12 = 2.91666666666667 hours