Work Problem

[jnellaz]

A union decided to build a home. The job can be done by 3 skilled workmen in 20 days or by 5 of the novice workers in 30 days. How many days will it take if all work together?

[spoiler]Answer: 12 days[/spoiler]

Pretty straightforward but I messed this one up by doing:

5/30 + 3/20 = 1
10/60 + 9/60 = 1
19/60 = 1 or 60/19 WRONG!

[logitech]

A union decided to build a home. The job can be done by 3 skilled workmen in 20 days or by 5 of the novice workers in 30 days. How many days will it take if all work together?

[spoiler]Answer: 12 days[/spoiler]

Pretty straightforward but I messed this one up by doing:

5/30 + 3/20 = 1
10/60 + 9/60 = 1
19/60 = 1 or 60/19 WRONG!

Let me try to give you a different approach.

Think the people as cars traveling with different velocities and the job done as distance, and the time to complete the job as the traveling time:

The job can be done by 3 skilled workmen in 20 days or by 5 of the novice workers in 30 days.

3S 20Days
5N 30 Days

so lets find the distance:

3Sx20days = 60Sdays

5Nx30days = 150Ndays

now remember they both travelled the same distance

60Sdays = 150Ndays

2S=5N

How many days will it take if all work together?

It actually means how long does it take for them to travel this distance if their velocities are added together!

we know the distance 150Ndays or 60Sdays ( SAME DISTANCE )

so lets pick one of them

60Sdays / (5N+3S) = ANSWER

60Sdays / ( 2S+3S) Remember 5N=2S

60Sdays / 5S

12 days! 8)

If you practice this method, you will find yourself doing this type of questions and many others VERY FAST!

[logitech]

A union decided to build a home. The job can be done by 3 skilled workmen in 20 days or by 5 of the novice workers in 30 days. How many days will it take if all work together?

[spoiler]Answer: 12 days[/spoiler]

Pretty straightforward but I messed this one up by doing:

5/30 + 3/20 = 1
10/60 + 9/60 = 1
19/60 = 1 or 60/19 WRONG!

but if you want to do with your method:

5N 30 days so 1 N 150 days
3S 20 days so 1 S 60 days

5(1/150) + 3(1/60) = 1/X

1/30 + 1/20 = 1/X

X = 12

OR METHOD III

And this is where you get confused

Think of 3 skilled workmen and 5 of the novice workers AS ONE COMBINED WORK UNIT, because they will work again together so

3s 20 days
5N 30 days

together ?

1/20 + 1/30 = 1/x

x = 12!

[jnellaz]

Dude, thanks again! I think you and I relate to this question. (Skilled worker versus novice)

[raunekk]

lets find the work done per day,

3 workmen takes 20 days= 1/20 th of work/day

5 workmen takes 30 days = 1/30th of work / day

wen work together= 1/20 + 1/30 th of work / day

= 1/12 th of work /day
= 12 days of total work

thanks

[cramya]

3 workers take 20 days 1 workers takes 60 days
5 workers take 30 days 1 woker takes 150 days

1/60 this is for 1 workers but since 3 workers are working it will be
1/60+1/60+1/60 or 3*1/60 = 1/20)


1/150 - this is for 1 worker but since 5 workers are working it will be
1/150 +1/150 +1/150 +1/150 +1/150 or 5*1/150 = 1/30)


When they work together u add the rates

rate*time = work

1/20+1/30 * t = 1
t=60/5 = 12 days

[jnellaz]

Wow...it seems the number of ways is endless. Thanks to you both! Cramya, great illustration!

[jaybrium]

I used the work formula:

if
a = the time it takes "a" to perform a task independently
and
b = the time it take "b" to perform the same task independently

then

ab / a + b = the time it takes both parties working together to perform "the task"

therefore;

if 3 skilled workers can build a house in 20 days; and
5 novices can build a house in 30 days; working together they can pull if off in

(20*30)/(20+30) = 12 days

the work formula can also be used if more than two parties are working together, just add variables. If there are 3 parties (a,b,c) working together then the time it takes them working together is:

abc / ab + ac + bc

I'm sure you can use it for 4 or more parties, but @ that point the formula will likely make things more complicated than necessary. I've never seen a simultanious work question that invovles four parties on the GMAT though... has anyone seen such a question?