1. ## Average/Rate/Time Word Problem.

The problem reads, If Art and Rita can do a job in four 4 hours when workin gtogether at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?

The problem is set up like this:

1/6 +1/R = 1/4

(R+6)/(6R) = 1/4

4R + 24 = 6R

R = 12

I totally understand how the problem is setup, but do not understand where the (R+6)/(6R) comes from? Then, I am totally in the dark as to how (R+6)/(6R) = 1/4 could work out to 4R + 24 = 6R!

Any, and I do mean ANY, help on this one would be great. I feel retarded because this one is so simple I do not know why I cannot figure it out.

Thanks!

2. ## Re: Average/Rate/Time Word Problem.

you do this by finding the lcm(lowest common multiple) of 6 and R which is 6R:
1/6 +1/R = 1/4

R/6R +6/6R=1/4

(R+6)/6R=1/4

Next you multiply the whole equation by 24R which is a common multiple of 6R and 4:
(R+6)/6R=1/4

24R(R+6)/6R=24R/4

4(R+6)=6R

4R+24=6R

24=2R

R=12

the whole thing could have been done this way:
1/6 +1/R = 1/4
1/R=1/4-1/6
1/R=6/24-4/24
1/R=2/24
1/R=1/12
R=12

3. ## Re: Average/Rate/Time Word Problem.

Originally Posted by Stoneface
The problem reads, If Art and Rita can do a job in four 4 hours when workin gtogether at their respective constant rates and Art can do the job alone in 6 hours, in how many hours can Rita do the job alone?

The problem is set up like this:

1/6 +1/R = 1/4

(R+6)/(6R) = 1/4

4R + 24 = 6R

R = 12

I totally understand how the problem is setup, but do not understand where the (R+6)/(6R) comes from? Then, I am totally in the dark as to how (R+6)/(6R) = 1/4 could work out to 4R + 24 = 6R!

Any, and I do mean ANY, help on this one would be great. I feel retarded because this one is so simple I do not know why I cannot figure it out.

Thanks!
$\frac{1}{6}+\frac{1}{R}=\frac{1}{4}$

ADDING FRACTIONS: Needs to have a common denominator.
$(\frac{R}{R}\cdot\frac{1}{6})+(\frac{1}{R}\cdot \frac{6}{6})=\frac{1}{4}$

$\frac{R}{6R}+\frac{6}{6R}=\frac{1}{4}$

$\frac{R+6}{6R}=\frac{1}{4}$

Clearing Fractions.

$6R\cdot\frac{R+6}{6R}=\frac{1}{4}\cdot6R$

Clearing Fractions.

$4\cdot{(R+6)}=\frac{6R}{4}\cdot4$

$4R+24=6R$

Now Solve for R and complete.