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
click here to see the step by step solution of the equation
the after person will need 3.56 hours to do the job alone.