Answered

Sumali sa IDNStudy.com at makakuha ng maraming kaalaman. Ang aming mga eksperto ay nagbibigay ng mabilis at eksaktong sagot upang tulungan kang maunawaan at malutas ang anumang problema.

it takes mary 3 hours more to do a job than its takes jane.If they work together, they can finish the same job in two hours.How long would its takes mary to finish the job alone?

Sagot :

Mlcparra16idn
We let the time that Jane takes to finish the job be x, so for Mary it is x+3.
This makes the rates of Jane and Mary be 1/x and 1/(x+3) respectively.
1/[1/x + 1/(x+3)] = 2
1 = 2/x + 2/(x+3)
1 = (4x+6)/(x²+3x)
x²+3x = 4x+6
x²-x-6 = 0

Method 1: Guess and Check
We look for two number with a product of 6 and an absolute difference of 1
6 - 1 = 5  X
3 - 2 = 1  √
So: (x-3)(x+2)=0
Therefore x is either 3 or -2 but we cannot have a negative time so we only consider 3. Therefore Mary's time is 6 hours. It takes her 6 hours to do it alone.

Method 2: Quadratic Formula
x = 1 ± √(1+24) = 1 ± 5 = -2 or 3
              2             2
Again, we cannot have a negative value. So Jane's time is 3 hours and Mary's is 6 hours. So the answer is 6 hours.
it will takes Mary to finish the job alone in 6 hours