Work Problem 6 Solution

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.

Work Problem 5 Solution

This is the solution to the work problem # 5 which read: Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?



Ok Tony takes 1 and 1/2 hours which is 90 minutes, and then we got jim at 30 minutes and Sue at 45 minutes. Convert everything to find out how much each can do in 1 minute. Tony does 1/90 th of his job in 1 minute Jim 1/30 th and Sue 1/45 th. So lets take just one individual persons job say Sue for example. If someone says Sue takes how long to finish her job if you know that she can do 1/45 of her job in a minute what would u say? 45 minutes. Or you can look at it as x/45 = 1 which means how many over 45 would = 1? The answer of course would be 45 again. So we set this problem up just like that only were ADDING the other peoples jobs together and setting it equal to 1.

So we got x/45 + x/90 + x/30 = 1 *Multiply both sides by 90 and get

2x + x + 3x = 90

6x = 90

x= 90/6 = 15

So it would take 15 minutes if all 3 worked together to finish the job.

Work Problem 4 Solution

This is the solution to the algebra work word problem # 4 which read: "Joe and Jim paint a house. Joe can paint it alone in 5 days, Jim in 8 days. They start to paint it together but after 2 days Jim stops. How long will Joe finish it alone?"

Joe takes 5 days
Jim 8
to paint a house

So Joe can do 1/5 of his job in one day and Jim can do 1/8th of his job in 1 day. If you just take Joe for example you can see where I'm heading on solving this problem. Joe can do 1/5th of his job in one day. So how long would he finish his job -- well besides knowing the answer already -- you would set it up as x/5 = 1. 1 being when the job is complete not just a "fraction" of his work being done. So the answer is 5 of course 5/5 = 1. You use this exact same method to solve the problem for both Joe and Jim.

**********Correction************ I realized I solved the problem before if they both continued working the job, but this problem states JIM stops working in 2 days. So Joe does x/5 part of his job in 2 days? 2/5 and Jim does x/8 part of his job in 2 days? 2/8, and Joe keeps working. So the equation would be

2/5 + 2/8 + x/5 = 1 multiply by 40 and get
16 + 10 + 8x = 40

26 + 8x = 40
8x = 40 - 26
8x = 14
x = 14/8 or 1 and 3/4ths so it would take 1 and 3/4ths days more for Joe to finish the job alone..

Tags: Work Problem Solutions, algebra word problem solutions

Work Problem 3 Solution

In this Algebra work problem solution we have a similar situation in dealing with hours and and figuring out how much of a job is done in 1 hour. The only difference is part of the job is being taken away -- negative --- by the leak. So just subtract this. That's the only difference between this work problem and the others.

So with Pump A in 1 hour it would 1/12th of a job Pump B would do 1/6th of a job and the leak would take away 1/24th of the job.

So algebraically we have:

x/12 + x/6 - x/24 = 1

multiply by 24

2x + 4x - x = 24

5x = 24

x = 24/5 or 4 and 4/5ths

4/5ths of an hour is 60*4/5 or 240/5 = 48 minutes

So the pool would be filled in 4 hours and 48 minutes.

Technorati Tags: Work Problem Solutions, Algebra Word Problem Solutions

Work Problem 2 Solution

This is the solution to the Algebra work problem # 2.

The key to solving any work problem is to figure out how much work can be done in 1 hour, minute, day- whatever time classification your using. In this problem it's talking hours. Since pump A takes 10 hours to finish then in 1 hours times 1/10th of the work would be complete and with the 8 hour pump B, 1/8th of the work would be done.

Now the way to understand this is to look at just 1 of the pumps. Take pump A for example. It takes 10 hours to fill the pool and 1/10 of the pool is finished in 1 hour. So ask yourself how many hours would it take a pump that fills 1/10th of a pool an hour to fill the entire pool? Or X/10 = 1 --- Without Algebra you know its 10 but using algebra you can see it works out the same way.

So all we do when were dealing with more than just 1 pump is to add their respective ratios together and set them equal to 1. We add because it's the added effect of both pumps that fills the pool.

So we have algebraically:

X/10 + X/8 = 1

multiply by 40 ----- the common denominator....

40X/10 + 40X/8 = 40

4X + 5X = 40

9X = 40

X = 40/9

X = 40/9 or 4 and 4/9ths

so almost 4 and a half hours. To get the exact minutes take 60 * 4/9 = 240/9 = 26 and 2/3rds

so we got 4 hours 26 minutes and if u want to be real anal 2/3's of a minute is 40 seconds (60 * 2/3 = 120/3 = 40)

So, it takes 4 hours 26 minutes and 40 seconds for pumps A and B to fill up the pool if they work together.

Technorati Tags: Work Problem Solutions, Algebra Word Problem Solutions

Work Problem 1 Solution

In this Algebra work word problem solution the way to figure out the answer is to realize that they work a fractional part of work each hour. So in 1 hours time Steve does 1/9 of his work, so in 9 hours he does 9/9 or his whole job. Same thing goes for Joe except he gets 1/10th of his job done in an hour. For just one guy, take Steve for instance, the algebra for his work by himself would be (1/9)x = 1 or x/9 = 1 which makes x = 9 or 9 hours. for Joe it would be x/10 = 1 or 10 hours. Together they would take x/9 + x/10 = 1 hours(x) to get the job done.

x/9 + x/10 = 1
multiply by 90
10x + 9x + 90
19x = 90
x = 90/19

90/19 = 4.74 or approximately 4 hours and 45 minutes (.75 would 3/4ths of an hour or 45 minutes). If you want it exact just take the fractional part(.7368) and multiply by 60. You'll end up with 44.2 which is 44 minutes and .2*60 seconds or 12 seconds. The detailed answer would be 4 hours 44 minutes and 12 seconds. So if he hires both of these guys he'll get the lawn mowed before 6 hours.