purplemath work word problem

[Bronn]

Im working thru on of the sites work problems here: http://www.purplemath.com/modules/workprob3.htm

Im fine all the way up until the end. I feel like Im missing something obvious, but its not clicking for some reason.

from the last section "finishing the job:"

20(1/100 + 1/120 + 1/t) = 0.45

20(11/600 + 1/t) = 0.45

11/600 + 1/t = 0.0225

im fine until here

1/t= 1/240

I can't figure out how the 240 came about.

when i try using fractions the whole time i get

20(11/600+1/t) = 9/20

11/600 +1/t = 9/400

i times each side by the reciprocal of 11/600 and get

1/t = 27/22

Which is obviously wrong.

Please help me out here


edit- DUH i minus the 11/600 *rolls eyes*

Ofcourse I couldn't figure this out for ages until I post this message. I need a break

 

[MarkFL]

If I was going to work that problem, I would first observe that in 10 hours, Maria could complete 6 tasks and Shaniqua can complete 5 tasks, and so together they can complete one task in 10/11 of an hour. So, after working together for 1/2 an hour they have 9/22 of an hour left or (9/22)(11/10) or 9/20 of the job left.

Now, let's suppose that in 10 hours, Liu can complete x tasks, so that the three ladies working together can complete one task in 10/(11 + x) of an hour. That means they can complete 9/20 of a task in 9/(2(11 + x)) of an hour, which we are told is 20 minutes, of 1/3 of an hour. Hence:

\(\displaystyle \displaystyle \frac{9}{2(11+x)}=\frac{1}{3}\)

\(\displaystyle \displaystyle 27=22+2x\)

\(\displaystyle \displaystyle x=\frac{5}{2}\)

So, in 10 hours Liu can complete 5/2 tasks, which means it takes her 10/(5/2) = 4 hours = 240 minutes to complete one task.

 

[HallsofIvy]

When two people work together their "rates of work" add. We are told that "Maria can complete the work in 100 minutes" so that Maria's rate of work is "one job per 100 minutes" or "1/100 job per minute". We are told that "Shaniqua can complete the same job in two hours" so Shaniqua's rate of work is "one job per 2 hours" or "1/2 job per hour".

Of course, we need to use the same units so either write Maria's rate of work as "3/5 job per hour" or write Shaniqua's rate of work as "1/120 job per minute". I think I will use "job per hour".

When Maria and Shaniqua work together the do 1/2+ 3/5= 5/10+ 6/10= 11/10 job per hour. They work together for 1/2 hour so they accomplish (11/10)(1/2)= 11/20 of the job with 9/20 left to do. Liu then joins them. Writing Liu's rate of work as "x", the rate of work of all three is 11/10+ x= (11+ 10x)/10 job per hour. At that rate they would accomplish 9/20 job in (9/20)/[(11+ 10x)/10]= (9/20)(10/(11+ 10x)= 9/(22+ 20x) hour. We are told that the three finished the job in 20 min= 1/3 hour so 9/(22+ 20x)= 1/3. We can write that as 27= 22+ 20x so that 20x= 27- 22= 5 and x= 5/20= 1/4 job per hour. Liu could do the entire task alone in 4 yours.