Combing Average of Person Doing X activity

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pj94z: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Tue Mar 20, 2007 12:22 pm

by pj94z » Wed Mar 21, 2007 7:09 am

bob paints house in 8 hrs by himself.

joe paints house in 6 hrs by himself.

how long will it take to paint the house together ?

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Source: Beat The GMAT — Problem Solving | Wed Mar 21, 2007 7:09 am

Neo2000: Legendary Member; Posts: 519; Joined: Sat Jan 27, 2007 7:56 am; Location: India; Thanked: 31 times

by Neo2000 » Wed Mar 21, 2007 7:45 am

In 1 hr Bob will pain 1/8th
and Joe will pain 1/6

Combined, in 1hr they will pain 1/8 + 1/6 = 14/48 = 7/24

which means they will take 24/7 hrs to paint the house

p.s. 1/8 = 12.5 and 1/6 = 16.6 approx 29% in 1hr to reach 100% will you need something over 3hrs but less than 4.

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pj94z: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Tue Mar 20, 2007 12:22 pm

by pj94z » Thu Mar 22, 2007 6:43 am

Neo2000 wrote:In 1 hr Bob will pain 1/8th
and Joe will pain 1/6

Combined, in 1hr they will pain 1/8 + 1/6 = 14/48 = 7/24

which means they will take 24/7 hrs to paint the house

p.s. 1/8 = 12.5 and 1/6 = 16.6 approx 29% in 1hr to reach 100% will you need something over 3hrs but less than 4.

- How do you get to the conclusion that it will take 24/7 hrs to paint the entire house? I understand they will do 7/24th of the house in 1 hour together, but how do u get 24/7 as the final answer?

- Is there any other method of solving this problem?

The answer choices are:

3 1/2

3 3/7

4

7

14

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Neo2000: Legendary Member; Posts: 519; Joined: Sat Jan 27, 2007 7:56 am; Location: India; Thanked: 31 times

by Neo2000 » Thu Mar 22, 2007 8:39 am

See in 1 hour they were doing 7/24 of the work W

In how many hours would they do the full work W??

Cross Multiplying gives you 24/7 hours

As for the shorter method, you could convert to decimals and continue.

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pj94z: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Tue Mar 20, 2007 12:22 pm

by pj94z » Thu Mar 22, 2007 8:55 am

Ahh...thanks for the clarification, I see it now:

You would setup as follows:

1 hr ....... x hr
-------- = ---------
7/24 w ..... 1 w

thanks for helping!

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Tame the CAT: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sun Mar 04, 2007 6:27 am

Re: Combing Average of Person Doing X activity

by Tame the CAT » Thu Mar 22, 2007 3:27 pm

pj94z wrote:bob paints house in 8 hrs by himself.

joe paints house in 6 hrs by himself.

how long will it take to paint the house together ?

Let's try this problem. Neo is right, but he skipped some steps and I can understand if you are confused.

First you want to convert the above into RATES

Bob takes 8 hours to finish 1 house which converts mathematically as 1 house per 8 hours or 1/8. That means Joe rate is 1/6.

Their combined rates is 1/8 + 1/6 = 14/48 = 7/24

The formula of Rate*Time = Work

We know what Rate and Work are - Work is 100% of 1 house and rate is 7/24

7/24*T = 1

T = 24/7

Pretty simple.

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Tue Mar 27, 2007 9:31 am

Here...Hope this helps...

1/8 + 1/6 = 7/24

Thus both of them working together can finish the work in 24/7

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