Question

Two teams of interns are wrapping donated gifts at a hospital. if the teams work alone, team a can wrap all of the gifts in 7 hours, and team b can wrap all of the gifts in 5 hours. how many hours will it take the interns to wrap all of the gifts if both teams work together? round the answer to the nearest half hour.

Answer 1

Together it would take 3 hours.
Team A can wrap all gifts in 7 hours; thus they can wrap 1/7 of the gifts in 1 hour.

Team B can wrap all gifts in 5 hours; thus they can wrap 1/5 of the gifts in 1 hour.

1/7h + 1/5h = 1, where h is the number of hours; it equals 1 because it is 100% of the gifts;

Find a common denominator.  35 is the first thing 7 and 5 will both divide into.  Convert the fractions:
5/35h + 7/35h = 1
12/35h = 1

Divide both sides by 12/35:
12/35h ÷ 12/35 = 1 ÷ 12/35
h = 1/1 ÷ 12/35
h = 1/1 × 35/12
h = 35/12
h = 2.9
h ≈ 3