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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?

how long together

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
1
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

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
4.8 4.8 (13 lesson ratings) (13)
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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