SOLUTION: . Bob takes 3 hours to mow a lawn. Al takes 4 hours. If they work together how long will it take?

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Question 999139: . Bob takes 3 hours to mow a lawn. Al takes 4 hours. If they work together how long will it take?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x = time it takes Bob to mow the lawn by himself (no one else helps)
y = time it takes Al to mow the lawn by himself (no one else helps)
z = time it takes Bob and Al to mow the lawn if they work together. This is assuming they work the most efficiently and don't get in each other's way

The values of x,y,z are times in hours

We're given "Bob takes 3 hours to mow a lawn. Al takes 4 hours" so

x = 3
y = 4
z = unknown but we can solve for it

1/x + 1/y = 1/z
1/3 + 1/4 = 1/z
4/12 + 3/12 = 1/z
7/12 = 1/z
12/7 = z/1
z/1 = 12/7
z = 12/7

If they work together, it takes exactly 12/7 hours which is approximately 1.714 hours (rounded to the nearest thousandth).