# Mr. A and Mr. B worked on a project for 42 hours. Mr. A worked three times longer than Mr. B. how long did Mr. B work on the project?

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• The answer is that Mr B worked 10.5 hours.

Here's how you get this answer.

Working step by step, find a way to express the times worked by each man.

In this case, it is easiest to begin with the number of hours worked by Mr B.

Let b equal the number of hours worked by Mr B.

b <-- the number of hours worked by Mr. B

Three times longer than that = 3b <-- the number of hours worked by Mr A

Together these amounts add up to 42 hours total

| Mr B's hours | plus | Mr A's hours | equals | the total number of hours

| . . . . .b . . . . .| . .+ . | . . . . .3b . . . .| . . = . . | . . . . . . 42

b + 3b = 42

Solve for b, already defined as "the number of hours worked by Mr B"

1) Combine like terms

4b = 42

2) Divide both sides by 4 to isolate b, already defined as "the number of hours worked by Mr B

b = 10.5 <-- the number of hours worked by Mr B

Three times more than that

31.5 <-- the number of hours worked by Mr A

CHECK

Mr B's hours . . 10.5

Mr A's hours . . 31.5

------------------------------

Total hours . . . .42.0

Check

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• A + B  =42

A+3A=42

4A=42

A=10.5

B=31.5

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