1. ## Working Together

Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

Let x = length of time it would them to deliver the newspapers working together

30 minutes = 1/2 hours

20 minutes = 1/3 hours

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

I found the answer to be (6/5) hours.

Is this correct?

I also found out that multiplying (2 × 3) and dividing by (2 + 3) leads to (6/5) hours.

Correct?

2. ## Re: Working Together

Originally Posted by harpazo
Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

Let x = length of time it would them to deliver the newspapers working together

30 minutes = 1/2 hours

20 minutes = 1/3 hours

(1/2) + (1/3) = (1/x)
I found the answer to be (6/5) hours.

Is this correct?
No, it is not! I hope that you realize that "5/6 hour" is longer than either "1/2 hour" or "1/3 hour"! Surely you understand that two people working together will not take longer than that either alone?

I also found out that multiplying (2 × 3) and dividing by (2 + 3) leads to (6/5) hours.

Correct?
When people or things "work together" their rates add. trent did this job (delivering newspapers) in 1/2 hour so was working at the rate of 1 job/(1/2) hour=2 job/hour. Lois did it in 1/3 hour so was working at 1 job/(1/3) hour= 3 job/hour. Together they work at 2+ 3= 5 job/hour. That means it will take them 1/5 hour per job together.

3. ## Re: Working Together

Originally Posted by HallsofIvy
No, it is not! I hope that you realize that "5/6 hour" is longer than either "1/2 hour" or "1/3 hour"!
It's worse than that. harpazo actually answered "(6/5) hours," which we see is longer than 5/6 hour.

4. ## Re: Working Together

Originally Posted by harpazo
Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

Let x = length of time it would them to deliver the newspapers working together

30 minutes = 1/2 hours

20 minutes = 1/3 hours

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

I found the answer to be (6/5) hours.

Is this correct?

I also found out that multiplying (2 × 3) and dividing by (2 + 3) leads to (6/5) hours.

Correct?
$$\dfrac{1}{ \left( \dfrac{1}{2} \right) }+\dfrac{1}{ \left( \dfrac{1}{3} \right) } = \dfrac{1}{x}$$

$$2+3 = \dfrac{1}{x}$$

$$x = \dfrac{1}{5}\text{ hr}$$

Alternately, keeping with minutes:

$$\dfrac{1}{30}+\dfrac{1}{20} = \dfrac{1}{y}$$

$$y = \dfrac{20\times 30}{20+30} = \dfrac{600}{50} = 12\text{ min}$$

Notice that $x=y$.

5. ## Re: Working Together

I understand what went wrong.