# If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?

They could complete the job together in

Sam: 4 days Lisa: 6 days Tom: 2 days

This is a "rate" problem. The rate is jobs per day, or job/day.

Multiplying through by the LCD gives:

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To find out how long it would take for Sam, Lisa, and Tom to complete the job together, you can use the formula:

1 / (Sam's rate) + 1 / (Lisa's rate) + 1 / (Tom's rate) = 1 / (Combined rate)

Sam's rate = 1 job / 4 days = 1/4 Lisa's rate = 1 job / 6 days = 1/6 Tom's rate = 1 job / 2 days = 1/2

1 / (1/4) + 1 / (1/6) + 1 / (1/2) = 1 / (Combined rate)

Solve for the combined rate:

1 / (1/4) + 1 / (1/6) + 1 / (1/2) = 6/24 + 4/24 + 12/24 = 22/24 = 11/12

So, the combined rate of Sam, Lisa, and Tom working together is 11/12.

Now, find out how long it would take for them to complete the job together:

Combined rate = 1 / (Time taken together)

11/12 = 1 / (Time taken together)

Time taken together = 12 / 11

So, it would take Sam, Lisa, and Tom ( \frac{12}{11} ) days to complete the job together.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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