# Work rate word problem

• Apr 5th 2005, 03:52 PM
Zerodollarbaby
Work rate word problem
Ray by himself can paint four rooms in 10 hours. If he hires Chris to help, together they can do the same job in 6 hours. If Ray lets Chris work alone, how long will it take for Chris to paint the four rooms?
• Apr 5th 2005, 05:09 PM
MathGuru
Welcome to MHF zerodollarbaby,

First lets figure out how fast ray works in rooms per hour.
Ray by himself can paint 4 rooms in 10 hours.
R = 4 rooms / 10 hours= 0.4 rooms/hour

Then lets figure out how fast ray and chris work together
R+C= 4 rooms/ 6 hours = .66' rooms/hour

Now lets subtract Ray's work rate from Ray and Chris' work rate

(R+C)-R=C
(.66')-(.4)=C
.266'=C

Chris paints at a rate of .266' rooms/hour
now divide the number of rooms by his work rate to find how many hours it would take him alone.

4 rooms / (.266' rooms/hour) ;rooms cancel and the unit becomes hours

Ans=15 hours
• May 26th 2007, 05:48 AM
janvdl
Quote:

Originally Posted by Zerodollarbaby
Ray by himself can paint four rooms in 10 hours. If he hires Chris to help, together they can do the same job in 6 hours. If Ray lets Chris work alone, how long will it take for Chris to paint the four rooms?

$Time(R_1 + R_2) = Job \ done$

$10(x) = 4$

$6(x+y) = 4$

$10x = 4x + 4y$

$y = \frac{4}{6} x$

$Set \ y's \ value \ into \ the \ equation$

$6(x + \frac{4}{6} x) = 4$

$x = 0,4$

$Set \ x = 0,4 \ into \ equation$

$6(0,4 + y) = 4$

$y = \frac{1}{15}$
• May 26th 2007, 06:03 AM
Soroban
Hello, Zerodollarbaby!

Here is yet another approach . . .

Quote:

Ray by himself can paint four rooms in 10 hours.
If he hires Chris to help, together they can do the same job in 6 hours.
If Ray lets Chris work alone, how long will it take for Chris to paint the four rooms?

Ray takes 10 hours to paint the rooms.
. . In one hour, he completes $\frac{1}{10}$ of the job.

Chris takes $x$ hours to paint the rooms.
. . In one hour, he completes $\frac{1}{x}$ of the job.

Together, in one hour, they can complete: . $\frac{1}{10} + \frac{1}{x}$ of the job.

But we are told that together it takes them 6 hours to paint the rooms.
. . In one hour, they can complete $\frac{1}{6}$ of the job.

There is our equation! . . . $\frac{1}{10} + \frac{1}{x}\:=\:\frac{1}{6}$

Multiply by $30x:\;\;3x + 30 \:=\:5x\quad\Rightarrow\quad 30 = 2x\quad\Rightarrow\quad x = 15$

Therefore, it will take Chris 15 hours to paint the rooms working alone.