One work crew can do a job in 8 days. After the first crew worked 3 days,
a second crew joins them, and together, the two crews finish the job in 3
more days. How long would it take the second crew to do the job alone?
i am confused how you would write the part where the second crew comes in after 3 days.?!?!?!?!?
thanks for all your help!
work problem
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- Rich@VeritasPrep
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Work = Rate * Time
w_1 = r_1 * t_1
w_1 = (1 job / 8 days) * (3 days)
w_1 = 3/8 job
There is 5/8 of the job left:
5/8 job = (r_1 + r_2) * 3
5/8 job = (1/8 + r_2) * 3
5/8 job = 3/8 + 3r_2
3r_2 = 1/4
r_2 = 1 job / 12 days
Answer: 12 days
Make sense?
w_1 = r_1 * t_1
w_1 = (1 job / 8 days) * (3 days)
w_1 = 3/8 job
There is 5/8 of the job left:
5/8 job = (r_1 + r_2) * 3
5/8 job = (1/8 + r_2) * 3
5/8 job = 3/8 + 3r_2
3r_2 = 1/4
r_2 = 1 job / 12 days
Answer: 12 days
Make sense?
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- Gurpinder
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raz1024 wrote:Work = Rate * Time
w_1 = r_1 * t_1
w_1 = (1 job / 8 days) * (3 days)
w_1 = 3/8 job
There is 5/8 of the job left:
5/8 job = (r_1 + r_2) * 3
5/8 job = (1/8 + r_2) * 3
5/8 job = 3/8 + 3r_2
3r_2 = 1/4
r_2 = 1 job / 12 days
Answer: 12 days
Make sense?
Hey raz,
I am sorry but I am still confused. I use the table method to solve these problems. can you please explain this one using the table method. (alone, rate,time,work).
your help is greatly appreciated.
- GMATGuruNY
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First, the rate formula. If r = rate, t = time, and w = work:Gurpinder wrote:One work crew can do a job in 8 days. After the first crew worked 3 days,
a second crew joins them, and together, the two crews finish the job in 3
more days. How long would it take the second crew to do the job alone?
i am confused how you would write the part where the second crew comes in after 3 days.?!?!?!?!?
thanks for all your help!
r * t = w.
Now a tip for work problems:
When the job is undefined, plug in your own number for the job.
Since the problem discusses a time of 8 days and a time of 3 days, the value of the job should be divisible by 8 and 3 in order to make the math easier. Let's say job = 24 bricks.
The first crew can complete the job of 24 bricks in 8 days. r = w/t = 24/8 = 3 bricks/day for the first crew.
The first crew works for 3 days. So it lays 3 bricks/day for 3 days. w = r * t = 3 * 3 = 9 bricks. So the first crew lays 9 of the 24 bricks. 24 - 9 = 15 bricks left to lay.
The two crews together to lay the remaining 15 bricks in 3 days. r = w/t = 15/3 = 5 bricks/day.
So when the 2 crews work together, they lay 5 bricks/day. We know that the first crew lays 3 bricks/day. So the second crew must lay 5 - 3 = 2 bricks/day.
Since we have 24 bricks, and the 2nd crew lays 2/day, to complete the whole job by itself the second crew will need t = 24/2 = 12 days.
Clear?
Last edited by GMATGuruNY on Thu Jul 08, 2010 8:05 am, edited 2 times in total.
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- kvcpk
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Let me explain a simple strategy for such problems.. The fractions are more confusing.Gurpinder wrote:One work crew can do a job in 8 days. After the first crew worked 3 days,
a second crew joins them, and together, the two crews finish the job in 3
more days. How long would it take the second crew to do the job alone?
i am confused how you would write the part where the second crew comes in after 3 days.?!?!?!?!?
thanks for all your help!
So let us forget fractions for sometime.
Take LCM of all the numbers you see in the question for days.
8 and 3 .. So LCM is 24.
Now, assume that there is 24 units of work to be done.
Let the workers be A and B.
It is given that A can complete the work in 8 days.
So 24 units can be done in 8 days implies that per day A does 3 units of work.
A worked for 3 days.
So how many units of work is over? 3*3units = 9 units.
How many units is left? 24-9 =15 units.
Now B joins A. Let us assume that B does x units per day.
then together they will do (x+3) units per day.
They completed the work together in 3 days.
So per day how many units they have done?
15/3 = 5 units per day.
so (x+3)=5 -> x=2
hence B can do 2 units per day.
Now we have 24 units. So B can complete the work in 24/2 = 12 days.
Hope this helps!! Let me know if you have any difficulty. Solving work-rate problems this way saves time and calculaltions are very easy.
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Thanks for the awsomeeee tip GmatGURUNY. "When the work is undefined, plugin a value." I will remember that.
@ kvcpk
thxx for the solution. your way of solving the problem or explaning how to solve it was reallyyyyyyy simple. I actually get it now.
The thing is, i have been doing math refreshing for some time now and every guide taught me to take the table approach:
i am in fact very very confortable using the table. would it be possible to tackle this problem using the table?
if so, can you please explain
thank you soo much
@ kvcpk
thxx for the solution. your way of solving the problem or explaning how to solve it was reallyyyyyyy simple. I actually get it now.
The thing is, i have been doing math refreshing for some time now and every guide taught me to take the table approach:
i am in fact very very confortable using the table. would it be possible to tackle this problem using the table?
if so, can you please explain
thank you soo much
Thank you, that is very clear. To make sure I'm getting this, let me ask a simpler question.
If Susie takes 4 hours to paint an entire house and Bob takes 3 hours to paint a house, how long would it take if they were to paint the house together?
Use the number 12 for work to simplify the math
r=12/4, so Susie paints portions of the house at a rate of 3 per hour
r=12/3, Bob paints at 4 per hour
together they paint at a rate of 4+3=7 per hour.
w=r*t
12=7*t
so it would take them 1.71 hours, so a little under 2 hours together?
If Susie takes 4 hours to paint an entire house and Bob takes 3 hours to paint a house, how long would it take if they were to paint the house together?
Use the number 12 for work to simplify the math
r=12/4, so Susie paints portions of the house at a rate of 3 per hour
r=12/3, Bob paints at 4 per hour
together they paint at a rate of 4+3=7 per hour.
w=r*t
12=7*t
so it would take them 1.71 hours, so a little under 2 hours together?
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silencz wrote:Thank you, that is very clear. To make sure I'm getting this, let me ask a simpler question.
If Susie takes 4 hours to paint an entire house and Bob takes 3 hours to paint a house, how long would it take if they were to paint the house together?
Use the number 12 for work to simplify the math
r=12/4, so Susie paints portions of the house at a rate of 3 per hour
r=12/3, Bob paints at 4 per hour
together they paint at a rate of 4+3=7 per hour.
w=r*t
12=7*t
so it would take them 1.71 hours, so a little under 2 hours together?
the problem you outline is a simple work problem silencz. this can be solved easily. the tricky thing with the one i posted was that one of the crew HAD already been working on a project for 3 days and the next crew joined them after 3 days.
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Perfect!silencz wrote:Thank you, that is very clear. To make sure I'm getting this, let me ask a simpler question.
If Susie takes 4 hours to paint an entire house and Bob takes 3 hours to paint a house, how long would it take if they were to paint the house together?
Use the number 12 for work to simplify the math
r=12/4, so Susie paints portions of the house at a rate of 3 per hour
r=12/3, Bob paints at 4 per hour
together they paint at a rate of 4+3=7 per hour.
w=r*t
12=7*t
so it would take them 1.71 hours, so a little under 2 hours together?
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One work crew can do a job in 8 days. After the first crew worked 3 days,
a second crew joins them, and together, the two crews finish the job in 3
more days. How long would it take the second crew to do the job alone?
after 3 days they do 3/8 of the job so have 5/8 of the job left
together they do 5/8 of job in 3 days
(5/8)/3 gives how much of the job they do in one day together.
they do 5/24 of the job per day together and one work crew does 1/8 or 3/24 of the job per day.
The second crew must do 5/24 - 3/24 of the job per day so 2/24 or 1/12 of the job per day.
Hence, they can do the entire job in 12 days.
a second crew joins them, and together, the two crews finish the job in 3
more days. How long would it take the second crew to do the job alone?
after 3 days they do 3/8 of the job so have 5/8 of the job left
together they do 5/8 of job in 3 days
(5/8)/3 gives how much of the job they do in one day together.
they do 5/24 of the job per day together and one work crew does 1/8 or 3/24 of the job per day.
The second crew must do 5/24 - 3/24 of the job per day so 2/24 or 1/12 of the job per day.
Hence, they can do the entire job in 12 days.