Jump to content
Urch Forums

Recommended Posts

Posted

I'm trying to solve the following work problem:

 

Working together, Andy and Bob can do a job in 6 days. Bob and Cindy can do the same job in 10 days. Cindy and Andy can do it in 7.5 days. How long will it take if they all work together?

 

I think the aim is to solve this equation:

1/A + 1/B + 1/C = 1/X

 

Therefore we have three further equations, haven't we?! ;)

1/A + 1/B = 1/6

1/B + 1/C = 1/10

1/C + 1/A = 1/7,5

 

Is there any possibility to solve this problem without using and transforming these three equations? (it takes a lot of time and I get some distorted numbers :( )

 

I were very happy if anybody could help me?!?

 

Thanks a lot...

Posted
I'm trying to solve the following work problem:

 

Working together, Andy and Bob can do a job in 6 days. Bob and Cindy can do the same job in 10 days. Cindy and Andy can do it in 7.5 days. How long will it take if they all work together?

 

I think the aim is to solve this equation:

1/A + 1/B + 1/C = 1/X

 

Therefore we have three further equations, haven't we?! ;)

1/A + 1/B = 1/6

1/B + 1/C = 1/10

1/C + 1/A = 1/7,5

 

Is there any possibility to solve this problem without using and transforming these three equations? (it takes a lot of time and I get some distorted numbers :( )

 

I were very happy if anybody could help me?!?

 

Thanks a lot...

 

Work = 1 job

Rate = Rate_A + Rate_B + Rate_C

Time = ?

 

So, we need to find the sum of the individual rates. This can be done by finding the value of each rate. Fortunately, we have three equations for three unknowns...we just need to set them up using work equations:

 

(Rate_A + Rate_B)*6 = 1

(Rate_C + Rate_B)*10 = 1

(Rate_A + Rate_C)*7.5 = 1

 

Matrix time!

 

Rate_A Rate_B Rate_C | RHS

1 1 0 | 1/6

0 1 1 | 1/10

1 0 1 | 1/7.5

 

Rate_A Rate_B Rate_C | RHS

0 0 1 | (1/6 - 1/10 - 1/7.5)/-2

0 1 0 | 1/10 + 1/2*(1/6 - 1/10 - 1/7.5)

1 0 0 | 1/7.5 + 1/2*(1/6 - 1/10 - 1/7.5)

 

Now we sum down the RHS values to get our new rate:

 

1/20+1/15-1/12 + 1/10 +1/12-1/20-1/15+1/7.5+1/12-1/20-1/15

=

1/20+1/12+1/15 = (3+5+4)/60 = 12/60 = 1/5

 

1 = 1/5*t

 

t = 5 days

Posted
I'm trying to solve the following work problem:

 

Working together, Andy and Bob can do a job in 6 days. Bob and Cindy can do the same job in 10 days. Cindy and Andy can do it in 7.5 days. How long will it take if they all work together?

 

I think the aim is to solve this equation:

1/A + 1/B + 1/C = 1/X

 

Therefore we have three further equations, haven't we?! ;)

1/A + 1/B = 1/6

1/B + 1/C = 1/10

1/C + 1/A = 1/7,5

 

Is there any possibility to solve this problem without using and transforming these three equations? (it takes a lot of time and I get some distorted numbers :( )

 

I were very happy if anybody could help me?!?

 

Thanks a lot...

 

Usually with stuff like this, the choices help make the problem easier. What choices were given?

Posted
I'm trying to solve the following work problem:

 

Working together, Andy and Bob can do a job in 6 days. Bob and Cindy can do the same job in 10 days. Cindy and Andy can do it in 7.5 days. How long will it take if they all work together?

 

I think the aim is to solve this equation:

1/A + 1/B + 1/C = 1/X

 

Therefore we have three further equations, haven't we?! ;)

1/A + 1/B = 1/6

1/B + 1/C = 1/10

1/C + 1/A = 1/7,5

 

Is there any possibility to solve this problem without using and transforming these three equations? (it takes a lot of time and I get some distorted numbers :( )

 

I were very happy if anybody could help me?!?

 

Thanks a lot...

 

DW: Just add all the three equations

 

2(1/A + 1/B + 1/C) = (5+3+4)/30 = 12/30

1/A + 1/B + 1/C = 1/5

 

Ans is 5.

  • 3 years later...
  • 4 weeks later...
Posted
I'm trying to solve the following work problem:

 

Working together, Andy and Bob can do a job in 6 days. Bob and Cindy can do the same job in 10 days. Cindy and Andy can do it in 7.5 days. How long will it take if they all work together?

 

I were very happy if anybody could help me?!?

 

Thanks a lot...

 

Lets take the total work to be 30 units...

 

A + B can do the total work in 6 days so in one day they can do (30 / 6) 5 units

 

B + C can do the total work in 10 days so in one day they can do (30 / 10) 3 units

 

A + C can do the total work in 7.5 days so in one day they can do (30 / 7.5) 4 units

 

 

Now add those

 

2 ( A + B + C ) in one day does ( 5 + 3 +4 )12 units

 

 

Now A + B + C produces 6 units ....

 

 

So they can complete the total work in 30 / 6 = 5 days...

 

 

Solved the problem without using equations and fractions...

  • 1 month later...
Posted

1/A + 1/B = 1/6 --------> 1/A = 1/6 - 1/B >>> (1)

1/B + 1/C = 1/10 -------> 1/B = 1/10 - 1/C >>> (2)

1/C + 1/A = 1/7.5 -------> 1/C = 1/7.5 - 1/A >>> (3)

 

1/A + 1/B + 1/C = 1/X

 

SUNSTITUTE equation (1), (2) & (3)

 

(1/6 - 1/B) + (1/10 - 1/C) + (1/7.5 - 1/A) = 1/X

[1/6 + 1/10 + 1/7.5] - [1/A + 1/B + 1/C] = 1/X

|_______________| |_____________|

2/5 - 1/X = 1/X

 

2/5 = 2/X

X = 5 days

  • 1 year later...
Posted
I'm trying to solve the following work problem:

 

Working together, Andy and Bob can do a job in 6 days. Bob and Cindy can do the same job in 10 days. Cindy and Andy can do it in 7.5 days. How long will it take if they all work together?

 

I think the aim is to solve this equation:

1/A + 1/B + 1/C = 1/X

 

Therefore we have three further equations, haven't we?! ;)

1/A + 1/B = 1/6

1/B + 1/C = 1/10

1/C + 1/A = 1/7,5

 

Is there any possibility to solve this problem without using and transforming these three equations? (it takes a lot of time and I get some distorted numbers :( )

 

I were very happy if anybody could help me?!?

 

Thanks a lot...

 

Ideal

{6*(A + B) - w, 10*(B + C) - w, (15*(A + C))/2 - w, (A + B + C)*d - w}={-5*w + d*w, 30*C - w, 15*B - w, 10*A - w}

{{A -> 0, B -> 0, C -> 0, w -> 0}, {B -> (2*A)/3, C -> A/3, d -> 5, w -> 10*A}}

 

d=5.

Posted

{6*(A + B) - w, 10*(B + C) - w, (15*(A + C))/2 - w, (A + B + C)*d - w}

{-5*w + d*w, 30*C - w, 15*B - w, 10*A - w}

{{A -> 0, B -> 0, C -> 0, w -> 0}, {B -> (2*A)/3, C -> A/3, d -> 5,

w -> 10*A}}

 

d=5.

Posted

idel

{6*(A + B) - w, 10*(B + C) - w, (15*(A + C))/2 - w, (A + B + C)*d - w}

={-5*w + d*w, 30*C - w, 15*B - w, 10*A - w}

{{A -> 0, B -> 0, C -> 0, w -> 0}, {B -> (2*A)/3, C -> A/3, d -> 5,

w -> 10*A}}

d=5.

  • 1 month later...
Posted
I'm trying to solve the following work problem:

 

Working together, Andy and Bob can do a job in 6 days. Bob and Cindy can do the same job in 10 days. Cindy and Andy can do it in 7.5 days. How long will it take if they all work together?

 

To avoid a lot of fractions, you can apply a number of "work units" to the entire job such that we're dealing with nice numbers.

Let's say that the entire job requires 30 work units (since 6, 10 and 7.5 all divide nicely into 30)

 

Let A = number of work units Andy can complete in 1 day

Let B = number of work units Bob can complete in 1 day

Let C = number of work units Cindy can complete in 1 day

 

Andy and Bob can do a job in 6 days: So, it takes them 6 days to complete 30 work units. That means they can complete 5 work units per day .

In other words, A+B=5

 

Bob and Cindy can do the same job in 10 days: So, it takes them 10 days to complete 30 work units. That means they can complete 3 work units per day .

In other words, B+C=3

 

Cindy and Andy can do it in 7.5 days: So, it takes them 7.5 days to complete 30 work units. That means they can complete 4 work units per day .

In other words, A+C=4

 

So, we have

A+B=5

B+C=3

A+C=4

 

Add them all together, to get 2A + 2B + 2C = 12

Divide both sides by 2 to get: A+B+C=6

In other words, all 3 people can complete a total of 6 work units each day.

If the total job is 30 work units, it will take them 5 days to complete the job

 

Cheers,

Brent

  • 2 weeks later...
Posted

LCM of 6 days, 10 days and 7.5 days is 30.

 

With that A+B=5

C+B=3 and

C+A=4

 

2(A+B+C)=12, therefore A+B+C=6. All of them together can complete in 6 days.

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Restore formatting

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...