# Thread: I need HELP FAST!!!

1. ## I need HELP FAST!!!

it takes Bill 2 hours longer to do a job than jerry. they work together for 2 hours; then jerry takes over and completed the job in 1 hour. how long would it take arch along to do the job?

2. Originally Posted by Brooke
it takes Bill 2 hours longer to do a job than jerry. they work together for 2 hours; then jerry takes over and completed the job in 1 hour. how long would it take arch along to do the job?
Let jerry completes the work in x hours, and bill in (x+2)hours
now, jerry works for 3 hous and bill for two hours to complete the job
hence,
$\displaystyle \frac{3}{x}+\frac{2}{x+2}=1$
$\displaystyle 3x+6+2x=x^2+2x$
$\displaystyle x^2-3x-6=0$

KeepSmiling
Malay

3. Hello, Brooke!

It takes Bill 2 hours longer to do a job than Jerry.
They worked together for 2 hours, then Jerry took over and completed the job in 1 hour.
How long would it take each alone to do the job?

Malay gave you an excellent explanation.
Let me give you my baby-talk version . . .

It takes Jerry $\displaystyle x$ hours to do the job alone.
. . In one hour, he can do $\displaystyle \frac{1}{x}$ of the the job.
He worked 3 hours, so he completed $\displaystyle \frac{3}{x}$ of the job.

It takes Bill $\displaystyle x + 2$ hours to do the job alone.
. . In one hour, he can do $\displaystyle \frac{1}{x+2}$ of the job.
He worked 2 hours, so he completed $\displaystyle \frac{2}{x+2}$ of the job.

Together, they competed the job ("1 whole job").
. . And there is our equation: . $\displaystyle \frac{3}{x} + \frac{2}{x+2}\:=\:1$

Multiply through by the LCD: $\displaystyle x(x+2):$
. . $\displaystyle x(x+2)\cdot\frac{3}{x} \:+ \:x(x+2)\cdot\frac{2}{x+2}\;\;=\;\;x(x+2)\cdot1$

We have: .$\displaystyle 3(x +2) + 2x \;= \;x(x + 2)$

. . which simplifies to the quadratic: .$\displaystyle x^2 - 3x - 6 \;= \;0$

. . Quadratic Formula: .$\displaystyle x\;=\;\frac{-(-3) \pm\sqrt{(-3)^2 - 4(1)(-6)}}{2(1)}$

. . and has the positive root: .$\displaystyle x \:= \:\frac{3 + \sqrt{33}}{2}$

Therefore: Jerry takes $\displaystyle \frac{3 + \sqrt{33}}{2}\:\approx\;4.37$ hours to do the job alone

. . . . and: Bill takes $\displaystyle \frac{7 + \sqrt{33}}{2}\:\approx\:6.37$ hours to do the job alone.