Question

Jack and Lucy can prepare a meal for a large party in 4 hours. Lucy alone can complete the job in 2 hours less time than Jack alone. Find the time that each person can prepare the meal alone.

Answer 1

Jack = 9.12 hours

Lucy = 7.12 hours

Explanation:

Given:

Jack + Lucy = 4 hours

Jack = x hours

Lucy = (x - 2) hours

From the statement we can propose the following equation:

`(1)/(x)+(1)/(x-2)=(1)/(4)`

We solve for x, like this:

`\begin{gathered} (x-2+x)/(x\cdot(x-2))=(1)/(4) \\ (2x-2)\cdot4=x\cdot(x-2) \\ 8x-8=x^2-2x \\ x^2-10x+8=0 \\ a=1 \\ b=-10 \\ c=8 \\ \text{ replacing in the general formula} \\ x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_1=\frac{-(-10)+\sqrt[]{(-10)^2-4\cdot1\cdot8}}{2\cdot1}=9.12 \\ x_2=\frac{-(-10)-\sqrt[]{(-10)^2-4\cdot1\cdot8}}{2\cdot1}=0.87 \end{gathered}`

The value cannot be 0.87 because it is a value below 4 hours, therefore, the value that it has here is 9.17 hours

Therefore:

Jack = 9.12 hours

Lucy = 7.12 (9.12 - 2) hours