SOLUTION: Derek rakes and bags the leaves of a lawn in 3 hrs. Alferd rakes and bags them in 5 hours. How long will it take to rake and bag the leaves if they do it together?

Question 3198: Derek rakes and bags the leaves of a lawn in 3 hrs. Alferd rakes and bags them in 5 hours. How long will it take to rake and bag the leaves if they do it together?
Answer by drglass(89) (Show Source): You can put this solution on YOUR website!
To solve this problem, you need to identify two things: the form of the answer and the facts you have to solve the problem.

Form of the answer:

The question is asking for the time it would take Derek and Alferd to rake the lawn and bag the leaves, so the answer should look like:

It would take them _____ hours to rake the lawn and bag the leaves.

To make this easier to write, we will treat raking and bagging as one thing, but when we answer the question, we have to remember to include both parts.

Facts:
1) It takes Derek 3 hours to rake the lawn
2) It takes Alferd 5 hours to rake the lawn

Next, we write the facts in a mathematical way:

Let's let the the letter D mean "the speed at which Derek can rake the lawn" so

means Derek can rake lawns per hour

We can also let A mean "the speed at which Alferd can rake the lawn," so

lawns per hour.

Notice that the facts don't relate directly to the problem. They tell us about speed but not time. This makes it a little more difficult to solve because we have to hope we can relate speed to time. Fortunately, we can do exactly that.

With our facts written in a mathematical way, we can solve the problem.
"The speed at which Derek and Alferd can rake the lawn" is written .So our solution begins

lawns per hour

We make both fractions take the same denominator by multiplying by and multiplying by . This gives us

lawns per hour

This almost answers the question. It tells us that Derek and Alferd can rake lawns per hour but, we need to know the time it takes them to rake one lawn. Let's call this time t.We can write this mathematically:

1 lawn raked = (lawns per hour) * ( hours)

If we divide both sides by , we get:

= t hours

So t = = = 1

So, our answer is:

It would take them 1 hours to rake the lawn and bag the leaves.

With practice, you will learn to do these steps by writing the problem mathematically, but for now, keep everything clear by writing it down.
RELATED QUESTIONS
"A mother can rake a yard in 90 minutes and her daughter can do it in 60 minutes.If the... (answered by josgarithmetic)

Phyllis can rake our lawn in 50 minutes and I can do it in 40 minutes. If she rakes for... (answered by stanbon,macston)

Nancy takes an hour and a half to rake the lawn. But it takes her only 40 minutes if her... (answered by stanbon)

candice rakes leaves for her neighbors. She charges $4 per hour to rake leaves plus $7 to (answered by fcabanski)

Andrea can rake her Dad's yard in 45 minutes. Andrea's brother Bradford rakes one and... (answered by ptaylor,nerdybill,Alan3354)

need to write an equation and solve Nancy takes an hour and a half to rake the lawn,... (answered by ikleyn)

Sam raked 3 bags of leaves in 16 minutes. if he continues to work at the same rate, about (answered by math_helper)

I have another question - Bert and Ernie working together can rake a lawn in 3 hours.... (answered by josmiceli)

George can rake a lawn in 5 hours. George and Juan together can rake the lawn in 2 hours. (answered by nerdybill)