Question

Three girls, Laura, Tammy, and Jeri, can wash the family cars, clean the pool, and mow the lawn in one hour and 20 minutes. If Jeri did all the work, she would take twice as long as Tammy and 2 hours longer than Laura. How long would Tammy take to do the job alone?

a) 3 hrs.
b) 4 hrs.
c) 6 hrs.

Answer 1

Answer: 3hours

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

Answer 2

Answer: it will take Tammy 3 hours to do the job. Option A

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