Problema Solution

Working together, two people can cut a large lawn in 2 hr.

One person can do the job alone in 1 hr less than the other.

How long would it take the faster person to do the job?

Answer provided by our tutors

let


x = hours that the first person needs to cut a large lawn alone

y = hours that the second person needs to cut a large lawn alone

let x < y (the first person is faster)


One person can do the job alone in 1 hr less than the other


x = y - 1


y = x + 1


Working together, two people can cut a large lawn in 2 hr


1/x + 1/y = 1/2


plug y = x+1 into the last equation


1/x + 1/(x + 1) = 1/2 multiply both sides by 2x(x + 1)


2(x + 1) + 2x = x^2 + x


4x + 2 + 2x = x^2 + x


x^2 - 5x - 2 = 0


by solving we find


x = 3.56 hr


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the after person will need 3.56 hours to do the job alone.