Answer: it will take Tammy 3 hours to do the job. Option A
Step-by-step explanation:
Let x be rate at which Laura will do the work.
Let x + 2 be rate for Jeri
Let 2 /(x + 2)be rate for Tammy
Rate of Job to be done = 1 -(1/3)÷2 = 3/4
Adding the rates together:
1/ x + (1/x+2) + 2/(x+2) = 3/4
Multiply both sides by 4x(x+2)
4(x+2) + 4x+ 8x = 3x(x + 2)
16x + 8 = 3x^2 +6x
3x^2 - 10x - 8= 0
Solving the quadratic equation you get:
3x(x-4) + 2(x -4)= 0
X=4
1. It will take Laura x= 4hrs to do the job
2. It will take Jeri x+2= 6 hrs to do the job
3. It will take Tammy 2/(x+2)= 3 hrs to do the job
Answer: 3hours
Step-by-step explanation:
Converting the given information into mathematical equation
Time taken and rate(reciprocal of time taken)
Laura = y hr/job , rate = 1/y job/hr
Jeri = y+2 hr/job , rate = 1/(y+2) job/hr
Tammy = (y+2)/2 hr/job , rate = 2/(y+2) job/hr
Total time taken if done together = 1 hour 20minutes per hour ;
80 minutes ÷ 60 minutes = 4/3 hr/job , rate = 3/4 job/hr
Combining the rate equation :
1/y + 1/y+2 + 2/y+2 = 3/4
Multiply through by 4y(y+2)
4(y+2) + 4y + 8y = 3y(y+2)
4y + 8 +4y + 8y = 3y^2+6y
16y + 8 = 3y^2 + 6y
3y^2 + 6y - 16y - 8 = 0
3y^2 - 10y - 8 = 0
3y^2-12y+2y-8 = 0
3y(y-4)+2(y-4) = 0
(y-4)(3y+2) = 0
(y-4)(3y+2) = 0
y = 4 or y = - 2/3
y has to be positive.
Therefore, you = 4
Tammy's time = (y+2)/2
(4+2)/2 = 3
