By herself, it takes Hillary 80 minutes to weed her backyard. One Saturday, after Hillary has been weeding for 32 minutes, her brother Steve helps and they finish after weeding together for 16 minutes. How long would it have taken if Steve weeded the yard by himself?

Let's start by finding out how much of the backyard Hillary can weed in one minute by dividing the total time she takes by the amount of work she does in that time

Hillary's rate = 1 backyard / 80 minutes = 1/80 backyard per minute

Now, we know that Hillary worked alone for 32 minutes, so she weeded:

Hillary's work = Hillary's rate x Hillary's time = (1/80 backyard per minute) x (32 minutes) = 0.4 backyards

We also know that Hillary and Steve weeded together for 16 minutes, so they weeded

Combined work = Combined rate x Combined time

We can set up an equation to solve for the combined rate

Combined rate = Combined work / Combined time

Combined rate = (Hillary's work + Steve's work) / 16 minutes

We know that Hillary and Steve weeded the entire backyard together, so

Combined work = 1 backyard

Substituting the values we know into the equation for the combined rate, we get

1/16 = (0.4 + Steve's work) / 16

0.4 + Steve's work = 1

Steve's work = 0.6

So Steve can weed 0.6 of a backyard in 16 minutes.

Now, we can use Hillary's rate to find out how long it would take Steve to weed the entire backyard by himself

Steve's time = Steve's work / Steve's rate

Steve's time = 1 backyard / (0.6 backyard per 16 minutes)

Steve's time = 26.67 minutes

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The given question is incomplete, the complete question is:

by herself, it takes hillary 80 minutes to weed her backyard. one saturday, after hillary has been weeding for 32 minutes, her brother steve helps and they finish after weeding together for 16 minutes. how long would it have taken if steve weeded the yard by himself?