how long together

## It takes lorraine 6 hours or Rocio 10 hour to complete a project alone. how long sould it take them to complete a project together?

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# 2 Answers

Lorraine's productivity is (1 project/6 hours) or 0.1667 projects per hour

Rocio's productivity is (1 project/10 hours) or 0.1 projects s per hour

If t is the time (in hours) it would take them to complete one project while working together, then

(0.1667 projects/hr)*t + (0.10 projects/hr)*t = 1

t*(0.1667 + 0.1) = 1

t*(0.2667) = 1

Therefore

**t = 3.75 hours**x=# of hours together to complete a project

Lorraine completes 1/6 of the project in an hour

Rocio completes 1/10 of the project in an hour

(1/6)x+(1/10)x=1(completed project)

multiply both sides of the equation by LCM of 6 and 10 which is 30

(30)[(1/6)x+(1/10)x]=30(1)

5x+3x=30

8x=30

x=3 and 6/8

x=3 and 3/4 or

x=3.75 hours