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A husband and wife started painting their house, but husband : GMAT Problem Solving (PS) - Page 2

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Re: A husband and wife started painting their house, but husband [#permalink]
08 Jul 2013, 05:48

1

This post received KUDOS

johnnybravo86 wrote:

A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?

A. 40/7 B. 50/7 C. 75/7 D. 55/7

1. In a normal scenario both the husband and wife would have taken 1/ (1/15+ 1/20) days = 60/7 days to complete the task 2. what did not happen was they definitely did not work together for 5 days. So subtract 5 days work together =5*7/60 = 7/12 th of the work 3. what did happen was the wife definitely worked alone for 5 days. So add 5 days of work of the wife = 5/15 = 1/3 rd of the work= 4/12 th of the work 4. From (2) and (3) we see 7/12- 4/12 = 3/12 th or 1/4 th of the work still remains. 5. this additional 1/4 th work would have been done by both because the wife worked alone for only 5 days which we have accounted for. So time taken for this work is 1/4 * 60/7 =15/7 6. Total time taken to complete the whole work in the altered scenario is 60/7 + 15/7 = 75/7 _________________

Re: A husband and wife started painting their house, but husband [#permalink]
07 Nov 2013, 11:41

Husband(working alone) completes the job in 20 days, implying a per day completion of 5% of total job Wife(working alone) completes the job in 15 days, implying a per day completion of 20/3% of total job

If we let the total no of days for work completion to be equal to 'T' days, then,

Wife works for all T days; husband works for T-5 days (leaves work 5 days before completion of work)

Setting up an equation for 100% completion of work -

Re: A husband and wife started painting their house, but husband [#permalink]
16 Nov 2013, 12:41

Hey johnnybravo86, whenever you come across such problems where you people work for different number of days or some days more or less, the best approach is to add up their individual work and not as a whole, In this problem, lets consider the work to be done as a single unit i.e. 1. now going according to the words of the question, let the wife work for x days. Thus, the husband works for x-5 days. Now their respective efficiencies(fraction of work done per day) are given as, H W 1/20 1/15 now simply multiply and add The final equation is

x/15 + (x-5)/20 = 1 solve for x, it comes out to be 75/7, which is the OA. Kudos me!

Re: Work & Rate problem [#permalink]
21 Nov 2013, 09:32

Bunuel wrote:

A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1: Rate of husband \frac{1}{20} job/day; Rate of wife \frac{1}{15} job/day; Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job; Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.

Could you possibly help me figure out why my method didn't work for solving:

I combined their two rates, and came up with \frac{7}{60} per day, so the whole job, combined, would have taken them \frac{60}{7}, or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \frac{25}{7}. The amount of work they completed was \frac{7}{60}* \frac{25}{7}=25/60 of the job. This leaves \frac{35}{60}of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her.

Re: Work & Rate problem [#permalink]
22 Nov 2013, 00:50

1

This post received KUDOS

Expert's post

AccipiterQ wrote:

Bunuel wrote:

A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1: Rate of husband \frac{1}{20} job/day; Rate of wife \frac{1}{15} job/day; Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job; Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.

Could you possibly help me figure out why my method didn't work for solving:

I combined their two rates, and came up with \frac{7}{60} per day, so the whole job, combined, would have taken them \frac{60}{7}, or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \frac{25}{7}. The amount of work they completed was \frac{7}{60}* \frac{25}{7}=25/60 of the job. This leaves \frac{35}{60}of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her.

If they work together they can complete the job in 60/7 days. But if one of them does not work for all that period then the time to complete would increase. Thus you cannot say that when husband left 5 days before, then they worked together for 60/7-5 days.

Re: Work & Rate problem [#permalink]
22 Nov 2013, 16:30

Bunuel wrote:

AccipiterQ wrote:

Bunuel wrote:

A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1: Rate of husband \frac{1}{20} job/day; Rate of wife \frac{1}{15} job/day; Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job; Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.

Could you possibly help me figure out why my method didn't work for solving:

I combined their two rates, and came up with \frac{7}{60} per day, so the whole job, combined, would have taken them \frac{60}{7}, or 8 4/7 days to complete. The husband left 5 days before this, so they worked together for 3 4/7 days, or \frac{25}{7}. The amount of work they completed was \frac{7}{60}* \frac{25}{7}=25/60 of the job. This leaves \frac{35}{60}of the job for the wife to complete alone. She can work at a rate of 4/60 per day. So that means she completed the remaining 35/60 in 8 3/4 days, not 5. This combined with the 3 4/7 that they worked on it together gives you a number of about 12.32, which is obviously not correct. Where did I go wrong? I'm having trouble reconciling how the wife only needed 5 days working at the rate given, when we can see how much work they did combined, and it leaves more than 5 days worth of work for her.

If they work together they can complete the job in 60/7 days. But if one of them does not work for all that period then the time to complete would increase. Thus you cannot say that when husband left 5 days before, then they worked together for 60/7-5 days.

Re: A husband and wife started painting their house, but husband [#permalink]
27 Apr 2014, 09:46

johnnybravo86 wrote:

A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?

A. 40/7 B. 50/7 C. 75/7 D. 55/7

Here's my simple solution.

Let total time taken for the job together = T Husband worked for days = T-5 Wife worked for days = T

Re: Work & Rate problem [#permalink]
28 Apr 2014, 02:39

Bunuel wrote:

A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days? A. 40/7 B. 50/7 C. 75/7 D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1: Rate of husband \frac{1}{20} job/day; Rate of wife \frac{1}{15} job/day; Combined rate: \frac{1}{20}+\frac{1}{15}=\frac{7}{60} job/day;

During the last 5 days, when the wife worked alone, she completed \frac{5}{15}=\frac{1}{3}rd of the job; Hence, remaining \frac{2}{3}rd of the job was done by them working together in time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7} days;

Total time needed to complete the whole job: 5+\frac{40}{7}=\frac{75}{7} days.

Answer: C.

Approach #2: It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \frac{7}{60} job/day, which means that working together they'll complete the job in \frac{60}{7} days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \frac{60}{7} days. Only \frac{75}{7} is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.

Approach # 2 definitely the smart way to think and work over here !!

gmatclubot

Re: Work & Rate problem
[#permalink]
28 Apr 2014, 02:39

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