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 J
eri 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.
Laura DATA: Time = x hr/job ; Rate = 1/x job/hr Jeri DATA Time = x+2 hr/job ; Rate = 1/(x+2) job/hr Tammy DATA: Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr. Together DATA: time = 4/3 hr/job ; Rate = 3/4 job/hr EQUATION: rate + rate + rate = together rate 1/x + 1/(x+2) + 2/(x+2) = 3/4 Multiply thru by 4x(x+2) to get: 4(x+2) + 4x + 8x = 3x(x+2) 16x + 8 = 3x^2+6x 3x^2-10x-8 = 0 3x^2-12x+2x-8 = 0 3x(x-4)+2(x-4) = 0 (x-4)(3x+2) = 0 Positive answer: x = 4 hrs. time for Laura to do the job x+2=6 hrs. time for Jeri to do the job (x+2)/2 = 3 hrs. time for Tammy to do the job
