<PRE><B>Question 3198</B>
To solve this problem, you need to identify two things: &lt;u&gt;the form of the answer and the facts you have to solve the problem.&lt;/u&gt;&lt;br&gt;
&lt;hr&gt;
Form of the answer:&lt;br&gt;
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:&lt;br&gt;

   It would take them _____ hours to rake the lawn and bag the leaves.&lt;br&gt;

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.&lt;br&gt;

&lt;hr&gt;
Facts:
1) It takes Derek 3 hours to rake the lawn
2) It takes Alferd 5 hours to rake the lawn&lt;br&gt;

Next, we write the facts in a mathematical way:&lt;br&gt;

Let&#39;s let the the letter D mean &quot;the speed at which Derek can rake the lawn&quot; so&lt;br&gt;
  {{{D = (1 lawn)/(3 hours)}}}&lt;br&gt;

means Derek can rake {{{1/3}}} lawns per hour&lt;br&gt;
We can also let A mean &quot;the speed at which Alferd can rake the lawn,&quot; so&lt;br&gt;
{{{A = 1/5}}} lawns per hour.&lt;br&gt;

Notice that the facts don&#39;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.&lt;br&gt;
&lt;hr&gt;

With our facts written in a mathematical way, we can solve the problem.&lt;br&gt; &quot;The speed at which  Derek and Alferd can rake the lawn&quot; is written {{{A + D}}}.So our solution begins&lt;br&gt;

{{{A + D = (1/3) + (1/5)}}} lawns per hour&lt;br&gt;

We make both fractions take the same denominator by multiplying {{{1/3}}} by {{{5/5}}} and multiplying {{{1/5}}} by {{{3/3}}}. This gives us&lt;br&gt;

{{{A + D = (5/5)(1/3) + (3/3)(1/5) = (5/15) + (3/15) = (5 + 3)/15 = 8/15}}} lawns per hour&lt;hr&gt;

This almost answers the question. It tells us that Derek and Alferd can rake {{{8/15}}} lawns per hour but, we need to know the time it takes them to rake one lawn. Let&#39;s call this time t.We can write this mathematically:&lt;br&gt;

1 lawn raked = ({{{8/15)}}}lawns per hour) * ({{{t}}} hours)&lt;br&gt;

If we divide both sides by {{{8/15}}}, we get:&lt;br&gt;

{{{1/(8/15)}}} {{{lawns/(lawns/hour)}}} = t hours&lt;br&gt;

So t = {{{1/(8/15)}}} = {{{15/8}}} = 1{{{7/8}}}&lt;br&gt;

So, our answer is:&lt;br&gt;

   It would take them 1{{{7/8}}} hours to rake the lawn and bag the leaves.&lt;br&gt;

With practice, you will learn to do these steps by writing the problem mathematically, but for now, keep everything clear by writing it down.</PRE>