<p>Okay, I don't understand this question:</p>
<p>Ester drove to wrok in the morning at the average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If ester spent a total of one hour commuting to an from work, how many miles did Esther drive to work in the morning?</p>
<p>The answer is 18. I have done a question like this before, with something with d=t x r</p>
<p>ya lol i am in the same boat. I actually learned rates after doing a problem.. then in the first BB test.. i came across this Grid in problem and blanked.</p>
<p>read the xiggi thread to preparing for the sat </p>
<p>There is a really simple formula for this kind of problem</p>
<p>(2<em>Speed1</em>Speed2)/(Speed1+Speed2)</p>
<p>(2<em>45</em>30)/(45+30)</p>
<p>(2700)/(75)</p>
<p>=36 miles total</p>
<p>36/2 = miles traveling 1 way = 18</p>
<p>Make sure that it's one hour before you use this formula</p>
<p>^ What if it more than one hour?</p>
<p>Also, why is it 18 and not 36?</p>
<p>rmadden15: When dealing with problems like this, it is a good idea to refer to the following formula: time = distance/speed (and you can switch it around as necessary). Once you have the formula down, ask yourself, "What information do I know?" In this case, you are given the speeds and the total time. Since you do not know the distance, just label it "x" or any other variable that makes you happy.</p>
<p>Considering that we know all but the distance, you can come up with the following equation: (x miles/45 miles per hour) + (x miles/30 miles per hour) = 1 hour</p>
<p>Here is how I got that equation: dividing x miles by 45 miles per hour gives you the time it must have taken to go to the destination, and dividing x miles by 30 miles per hour gives you the time it must have taken to return from the destination (both trips, going there and coming back, produce equal distances—x and x). Since both of these added give you the total time of the trip, have the sum of these two terms equal 1 hour, which is the total time. I hope I've answered your question. =D</p>
<p>2t(r1 * r2) = d
...(r1 + r2)</p>
<p>t = time (in relation to rate, i.e., in hours if mph)
r = rate (speed in relation to time)
d = total distance traveled both ways
ignore the "..."</p>
<p>Rate x Time = Distance </p>
<ol>
<li><p>The rate going to work we know as 45 MPH. We don't know the time, so we assign the time X. Using (R)(T)=D formula, we get the distance of the commute to work as 45X. </p></li>
<li><p>For the commute FROM work, the time spent for her way back is going to be 1-x, because we know that her total commute is 1 hour. Moreover, we know her rate is 30 MPH. So, we get the (R)(T)=D formula's gonna be
(30)(1-x), which is 30-30X. </p></li>
<li><p>Now, we know that she travelled the SAME route. So, 30-30X is the same distance as 45X. Therefore, 30-30X=45X. Solve for X and you get X=30/75=6/15.</p></li>
<li><p>We've only solved for X, which is the time of the first leg of the trip. So plug in the number, rate (45) multiplied by time (6/15)= 18 miles.</p></li>
</ol>
<p>Thanks everyone....I almost have it. I am kinda slow when it comes to math. :)</p>
<p>the answer is 18 and not 36 because 36 is the total distance traveled BOTH ways. the question asks how many miles did Esther travel in the MORNING (aka one way), so that is half the distance, (36/2 = 18)</p>
<p>Wow! Is this from the blue book? Because I was taking a practice test with my tutor the other day and came across this question on the student produced responses and couldnt figure it out, so I made a complete guess and said 17! AHH so close.</p>