Question

If Terri were to paint her living room alone, it would take 6 hours. Her sister Gloria could do the job in 7 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.

Please help

Answer 1

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➷ Add together the values as fractions:

1/6 + 1/7 = 13/42

Take the reciprocal:

42/13 is the answer

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Answer 2

C = 42/ 13 hours or 3 3/13 hours

Explanation:

The formula is

1/A +1/B = 1/C

where A is the time for person 1 to do the job alone

B is the time for person B to do the job alone

C is the time for them to do the job together

1/6 + 1/7 = 1/C

The common denominator is 42C so multiply each side by 42C

42 C*(1/6 + 1/7) = 1/C *42C

Distribute

7C +6C = 42

13 C = 42

Divide each side by 13

C = 42/13

Changing to a mixed number

C = 3 3/13 hours