landscaper

Question

They are looking for the equation that best represents the situation.

a landscaping crew is using 3 different lawnmowers to cut a large lawn. lawnmower A can cut the entire lawn by itself in 4 hours. Lawnmower B takes twice as long as lawnmower C. If all three mowers are used to cut the grass, the entire job will only take 2 hours. How fast can lawnmower B cut the grass?

Answer 1

The rate for lawnmower A is 1/4 lawn in an hour.

 

If lawnmower C takes h hours to do the lawn by itself, then lawnmower B takes 2h hours working alone.

Then C can do 1/h of the lawn in an hour and B can do 1/(2h) of the lawn in an hour.

 

When lawnmowers A, B, C work together, in an hour they do 1/4 + 1/h + 1/(2h) = 1.4 +3/(2h)

Working together they do the whole lawn in 2 hours, or 1/2 the lawn in an hour.

 

Equating these rates, 1/4 + 3/(2h) = 1/2

                               (3/2h) = 1/4

                               h = 12/2 = 6 hours

 

Lawnmower B takes 12 hours to mow the whole lawn by itself.