Q:

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?3 hrs.4 hrs.6 hrs.

Accepted Solution

A:
Answer: it will take Tammy 3 hours to do the job. Option AStep-by-step explanation:Let x be rate at which Laura will do the work.Let x + 2 be rate for JeriLet 2 /(x + 2)be rate for TammyRate of Job to be done = 1 -(1/3)Γ·2 = 3/4Adding the rates together:1/ x + (1/x+2) + 2/(x+2) = 3/4Multiply both sides by 4x(x+2)4(x+2) + 4x+ 8x = 3x(x + 2)16x + 8 = 3x^2 +6x3x^2 - 10x - 8= 0Solving the quadratic equation you get:3x(x-4) + 2(x -4)= 0X=41. It will take Laura x= 4hrs to do the job2. It will take Jeri x+2= 6 hrs to do the job3. It will take Tammy 2/(x+2)= 3 hrs to do the job