# Thread: Working Together

1. ## Working Together

Mary Ann can deliver her newspapers in 30 minutes. It takes Ginger 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

I know that 30 minutes is 1/2 of an hour.
I also know that 20 minutes is 1/3 of an hour.

Let x = time for both girls to work together

My Equation:

(1/2) + (1/3) = 1/x

Is this the correct equation?

2. ## Re: Working Together Originally Posted by harpazo Mary Ann can deliver her newspapers in 30 minutes. It takes Ginger 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

I know that 30 minutes is 1/2 of an hour.
I also know that 20 minutes is 1/3 of an hour.

Let x = time for both girls to work together

My Equation:

(1/2) + (1/3) = 1/x

Is this the correct equation?
No, for a few reasons:

1. If you solve this equation you will get x = 6/5. Does that give you the correct answer?? No, because that would mean 1 hour 12min.
If they are working together they will take less than 20 min (which is how long Ginger can do it on her own).

2. Look at the units.
On the LHS, you have hours + hours (which will give hours).
On the RHS, your "units" are 1/hour.

If the units are not the same then the expressions can not be equal.

Have another go at this one.

3. ## Re: Working Together Originally Posted by harpazo Mary Ann can deliver her newspapers in 30 minutes.
It takes Ginger 20 minutes to do the same route.
How long would it take them to deliver the newspapers if they work together?
Trick:
Make the job delivering 60 papers; so:
Mary: 2 papers per min
Ginger: 3 papers per min
Combined: 5 papers per min

Get my drift?

4. ## Re: Working Together Originally Posted by DenisB Trick:
Make the job delivering 60 papers; so:
Mary: 2 papers per min
Ginger: 3 papers per min
Combined: 5 papers per min

Get my drift?
So, 60 papers ÷ by 5 papers per minutes = 12 minutes.

Together, they can do the job in 12 minutes.

5. ## Re: Working Together Originally Posted by Debsta No, for a few reasons:

1. If you solve this equation you will get x = 6/5. Does that give you the correct answer?? No, because that would mean 1 hour 12min.
If they are working together they will take less than 20 min (which is how long Ginger can do it on her own).

2. Look at the units.
On the LHS, you have hours + hours (which will give hours).
On the RHS, your "units" are 1/hour.

If the units are not the same then the expressions can not be equal.

Have another go at this one.
I got 12 minutes for both to complete the job together following DeniB's break down. However, I would like to know what the proper equation is for this question.

6. ## Re: Working Together

x = Mary's time, y = Ginger's time

Together: 1 / (1/x + 1/y) = 1 / (1/30 + 1/20) = 1 / (2/60 + 3/60) = 1 / (5/60) = 60/5 = 12

7. ## Re: Working Together Originally Posted by DenisB x = Mary's time, y = Ginger's time

Together: 1 / (1/x + 1/y) = 1 / (1/30 + 1/20) = 1 / (2/60 + 3/60) = 1 / (5/60) = 60/5 = 12
Nicely done! Thanks.

8. ## Re: Working Together Originally Posted by Debsta No, for a few reasons:

1. If you solve this equation you will get x = 6/5. Does that give you the correct answer?? No, because that would mean 1 hour 12min.
If they are working together they will take less than 20 min (which is how long Ginger can do it on her own).

2. Look at the units.
On the LHS, you have hours + hours (which will give hours).
On the RHS, your "units" are 1/hour.

If the units are not the same then the expressions can not be equal.

Have another go at this one.
1/20 + 1/30 = 1/x

Let x = the time they work together

Multiply both sides by 60.

(3 + 2) = 60/x

5 = 60/x

5x = 60

x = 60/5

x = 12

9. ## Re: Working Together Originally Posted by harpazo So, 60 papers ÷ by 5 papers per minutes = 12 minutes.

Together, they can do the job in 12 minutes.
Damn, why did I never think of this? I always do it like this: Originally Posted by DenisB x = Mary's time, y = Ginger's time

Together: 1 / (1/x + 1/y) = 1 / (1/30 + 1/20) = 1 / (2/60 + 3/60) = 1 / (5/60) = 60/5 = 12

10. ## Re: Working Together

Thank you everyone.