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.
work problem- how to solve
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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
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
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The math itself is brutal and well beyond what you're expected to do on the GMAT.ershovici wrote:How did you solved this equation?gmat.2008 wrote: (1/t)+(1/t-2)=(1/6)
on solving, t=13.1
so t-2=11.1
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.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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