work problem- how to solve

[kartik1979]

Kamil and Anita are typing a manuscript. Anita can type it in 2 hours less time than Kamil. Together they can do the job in 6 hours. How long will it take Anita if she works alone? Give your answer to the nearest tenth

ans given is Kamil taking 13.1 hours and Anita taking 11.1 hours.

[gmat.2008]

lets say Kamil takes 't' hrs then Anita will take 't-2' hrs.

together they take 6hrs

so, kamil's 1hrs work =(1/t) similarly anita's 1hrs work = (1/t-2)

together in 1 hr they can complete 1/6 th work

(1/t)+(1/t-2)=(1/6)

on solving, t=13.1

so t-2=11.1

[ershovici]

(1/t)+(1/t-2)=(1/6)

on solving, t=13.1

so t-2=11.1

How did you solved this equation?

[aspirant1]

Pls, put in the answer choices...wondering if we can plug-in

[Stuart@KaplanGMAT]

(1/t)+(1/t-2)=(1/6)

on solving, t=13.1

so t-2=11.1

How did you solved this equation?

The math itself is brutal and well beyond what you're expected to do on the GMAT.

We end up with the quadratic:

t^2 - 14t + 12 = 0

and, short of using a calculator, I have no idea how the person solved to 13.1 in a reasonable amount of time. If we had to do so, we could set up simultaneous equations:

a * b = 12

and

a + b = -14

and our solution would appear as:

(t + a)(t + b) = 0

and after the math, would appoximate to:

(t - 13.1)(t - .9) = 0

(Note: we actually get t=13.1 or t=.9; however, we can eliminate t=.9 because then t-2 would be negative, which is impossible.)

Backsolving would definitely be much quicker on this question.