This is the solution to Work Problem 6 which asked, "A mother can rake a yard in 90 minutes and her daughter can do it in 60 minutes.If the mother rakes for 15 minutes before her daughter joins her,how long will it take them to finish the work?"

Ok the mother can do 1/90th of her job in a minute so if you have x/90 in 90 minutes 90/90 = 1 she completes her job same thing goes for the the daughter .. 1/60 of her job done in a minute with x/60 in 60 minutes 60/60 = 1 she completes her job. Seems kind of silly that I'm pointing this out but this is how you solve the problem you just add their work together and set it equal to 1. Their is one additional stipulation in the problem though and thats the mother starting 15 minutes before the daughter joins the mother otherwise it would just be

x/90 + x/60 = 1... but the mother rakes for 15 minutes and completes 15/90 of her job so the way to write it out would be x/90 + 15/90 + x/60 = 1.

multiply everything by 180 and get 2x + 30 + 3x = 180.

5x + 30 = 180

5x = 150

x = 30 So it would take 30 minutes if they worked together. **UPDATE**: "how long will it take **them** to finish the work?" <-- Sounds to me like how long will they finish together thus 30 minutes the answer. But if you want to take this to mean how long did it take them to finish the total job then add the 15 minutes of initial work done by the mother which would be 30 + 15 = 45.

## Thursday, November 25, 2010

### Work Problem 6 Solution

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I'm 9 years old and i did this promblem in 7.23 minutes. Boogie Woogie!

ReplyDeleteNice-- How long would it have taken if you would have done the problem with someone else who could have solved it in 3.28 minutes? lol

ReplyDeletehaha!

ReplyDeletewow its hard :D

nice work sir it really helpfull

ReplyDeleteok..

ReplyDeleteIt's very easy I answer it for just 5 seconds.

ReplyDeletewhy does it needs to multiply by 180??

ReplyDeleteOH...THAT'S QUIET EASY

ReplyDeleteI'm challenging my self and i want some problems like this. Thank you! It took me 1 minute or 2 minute. Don't be so arrogant, Paul.

ReplyDelete,,,,,it's brain teaser.

ReplyDeletecan you help me how to pass in my algebra subject

ReplyDeleteits not correct.. you can check the problem 4,

ReplyDeleteits almost the same as this

so the equation for this will be:

15/90 + 15/60 + x/60 = 180

30 + 45 + 3x = 180

75+3x=180

3x=180-75

3x=105

so it will be 35minutes.

Sorry but you are wrong -- Your equation would be for the problem "A mother can rake a yard in 90 minutes and her daughter can do it in 60 minutes.If the mother and daughter rake for 15 minutes together before her daughter works alone, and the mother stops raking, how long will it take the daughter to finish the work?" Unfortunately, that is not the problem. The problem is "A mother can rake a yard in 90 minutes and her daughter can do it in 60 minutes.If the mother rakes for 15 minutes before her daughter joins her,how long will it take them to finish the work?"

ReplyDeleteis that correct or true because i will be use it from my project i was just concern...

ReplyDeletethank you.........

It's correct/true. Feel free. I can show you why it's correct if you like.

ReplyDeleteit says the mother can do the job for 90minutes and the daughter for 60 minutes then before they start the mother made her first 15minutes so it means 15minutes before they both do the job are done, its almost the same to say that the mother can finish it in 90-15=75 minutes. its like

ReplyDelete1/75 + 1/60 = 300

1/75 = 4, 1/60 = 5,

4+5=9

300/9 = 33.33 or 33minutes and 20seconds

Sorry kulokoy- but that is not correct.. Yes she would finish in 75 minutes but if her rate was 1/75 a minute she wouldn't have gotten the same amount of work covered in 15 minutes initially. She got that much work done initially because her rate was 1/90 not 1/75 thus why your answer is a little off. Here's a way of looking at it... Lets say you got 2 people who can finish a job in 60 minutes -> so if they worked together they would finish in 30 minutes right? -- x/60 + x/60 = 1 ---> 2x = 60 --> x = 30 ok now lets say 1 of them does 30 minutes of work 1st -- ya that would mean that the 1 person would have just 30 minutes work or x/30 rate for the REST of the job but it doesn't work out correctly because you have to be consistent on the rates throughout or the math doesn't work. For example if you do it your way you would say one person only has x/30 of the job left and the other x/60 . You can already see how this won't work out. x/30 + x/60 = 1 2x + x = 60 3x = 60 x = 60/3 = 20 but the answer should be 15 minutes since its half of hour the working together. Should be 30/60 + x/60 + x/60 = 1 --> 30 + x + x = 60 ---> 2x = 60 - 30 ---> 2x = 30 --> x = 15 which makes sense. If it takes them 30 minutes to an hour job together it would take them only 15 minutes or half of that to do a 30 minute job together not 20 minutes....

ReplyDeletethis is wrong.. refer to this one http://www.indiabix.com/aptitude/time-and-work/discussion-403

ReplyDeleteyou first need to get the work done by the mother in 15mins so 1/90 * 15 = 1/6

1/6 work done by 15mins

1 - 1/6 = 5/6 work left

1/90 + 1/60 = 5/180 or 1/36 work made by both

so 1/6 * 1/36

= 6/36 or 6 minutes

now 6minutes + 15minutes done = 21 minutes

the work last for 21 minutes

Sorry anon that is incorrect. I think you might be reading the problem incorrectly because you start off correct but you add a unnecessary step. Ya the mother works for 15 minutes 1/90 * 15 = 1/6 correct Yes 1 - 1/6 5/6 work left correct. Yes 1/90 + 1/60 = 5/180 or 1/36 work done together. But THIS is all you need. You already KNOW how much work is left for them BOTH to work together which is 5/6 and their rate is x/36 together to finish that job. So it's x/36 = 5/6 . Multiply by 36 and you get x = 30 which is my answer.

ReplyDeleteTo prove my answer is correct try this. Lets say two people take 60 minutes separately to finish a job-- so x/60 work rate for both. Now lets say one of them goes in and works for 30 minutes. That leaves 1/2 or 30 minutes of the job left. So if it takes them 60 minutes to do the job themselves then together and it takes them 30 minutes to do a full job together THEN it makes sense that it would only take them 15 minutes to do half of that job together right? So let me set this up exactly how I set up my problem. 30/60 + x/60 + x/60 = 1

30 + x + x = 60

2x = 30

x = 15 or doing it the way you set it up in yours x/30 = 1/2

2x = 30 x = 15

In your problem you did a unnecessary step "so 1/6 * 1/36

= 6/36 or 6 minutes

now 6minutes + 15minutes done = 21 minutes

the work last for 21 minutes " I don't know what you are doing here possibly you read the problem wrong but either way 1/6 * 1/36 does not equal 6/36

Anon I checked that site. They are taking the fraction of the job left and multiplying it by the inverse of the total work for both done between the two in one day. You multiplied the the work done by the mom which was 1/6 where you should have done the total work left which is 5/6 and multiplied that by 36 which is the inverse 1/36 the total work done in 1 day by both. 36 * 5/6 = 30 and if you want to take this problem to mean the total time for the WHOLE job to be completed then add the 15 minutes to that as well which would make it 45 for the whole job.

ReplyDelete