At Pizza Perfect, Ron and Harold make pizza crusts. When they work separately Ron finishes the job of making 100 crusts 1.2 hours before Harold finishes the same job. When they work together they finish making 100 crusts in 1.8 hours. How many hours, to the nearest tenth of an hour, does it take Ron working alone to make 100 crusts?

macar0ni Apr 2, 2021

#1**+1 **

Ron takes approximately $\boxed{4.2}$ hours to make $100$ crusts alone.

Since we are given that:

Number of hours taken by Ron before Harold = 1.2 hours

Number of hours taken by Ron and Harold together = 1.8 hours

We need to find the number of hours taken by Ron alone i.e. $'x'$.

Let the number of hours taken by Harold alone be $'1.2-x'$.

Let the work done by Ron alone=$1/x$

Let the work done by Harold alone=$1/(x-1.2)$

We get that:

$\frac{1}{x}+\frac{1}{x-1.2}=\frac{1}{1.8}$

$\frac{x-1.2+x}{x(x-1.2)}=\frac{1}{1.8}$

$\frac{2x-1.2}{x^2-1.2x}=\frac{1}{1.8}$

$3.6x-2.16=x^2-1.2x$

$x^2-1.2x-3.6x+2.16=0$

$x^2-4.8x+2.16=0$

$(x-0.5)(x-4.2)=0$

$x$ can be either $0.5$ or $4.2$ to satisfy the equation

$x-1.2$ is negative with $x = 0.5$, so $x = 4.2$ is the only solution

Hence, Ron takes approximately $\boxed{4.2}$hours to make 100 crusts alone.

RiemannIntegralzzz Apr 2, 2021

#2**+1 **

thank you so much for your efforts! however, it says that your answer is wrong. though i read your solution and i can't see any flaws...

macar0ni
Apr 2, 2021

#3**+1 **

@macar0ni What was the answer/solution that the book/platform/whatever gave?

RiemannIntegralzzz
Apr 2, 2021

#5**+1 **

Let x be the number of hours it takes Ron working alone = 1/x = rate

Then x + 1.2 = the number of hours that Harold takes to finish the job alone = 1/ ( x + 1.2) = rate

So rate * time = 1 whole job done....so....

1.8 ( 1/x) + 1.8 (1/ ( x + 1.2) ) = 1

1.8 1.8

___ + ______ = 1 simplify

x x + 1.2

1.8 ( x + 1.2 + x) = x ( x + 1.2)

2.16 + 3.6x = x^2 + 1.2x rearrange as

x^2 - 2.4x - 2.16 = 0

Using the quad formula

x = 2.4 + sqrt (2.4^2 - 4 (1)(-2.16) ) ≈

____________________________

2

3.09 hrs = 3.1 hrs for Ron working alone

CPhill Apr 2, 2021

#9**0 **

**No, RiemannIntegralzzz, you don’t see where you went wrong! You might see where Windy York went wrong, because this is her work, not yours. Where you went wrong is when you plagiarized Windy’s solution and comments –nearly word for word. You didn’t bother checking if it was the correct answer.**

Guest Apr 2, 2021

edited by
Guest
Apr 2, 2021

#10**0 **

Hi Riemann,

I have looked at the link and this certainly does look plagiarized to me as well.

I have no problem with you finding and presenting answers from elsewhere but you must give people credit for their work.

You can take credit for finding an answer, and that is a skill in itself, but don't take producing an answer when you have not done so.

Melody
Apr 3, 2021