<p>A woman drives to work. On the trip to work she drives 45 mph. On the way home she drives 30 mph. It takes her one hour (round trip). How far did she drive to work?</p>
<p>This is a toughie.</p>
<p>Thanks!</p>
<p>One of the easiest possible questions.
45x = 30 (1-x)
45x=30-30x
75x=30
x=2/5
2/5 hours = 24 minutes ,so she goes to work in 24 minutes and drives back for 1 - 2/5=36 minutes
Her way to work is 45x2/5 = 18 km</p>
<p>The distance she drove in the morning is the same as the distance she drove in the afternoon.</p>
<p>We know the rates (speeds), we need to know the miles. We can do this by manipulating the units. We know that driving at 40miles/hour + driving at 30 miles/hour = X distance/ 1 hour.</p>
<p>So we need to manipulate it so that miles/hour + miles/hour = hour. In order to do so, you have to cancel out the miles so that hour + hour = hour. You can do that by multiplying by 1/mile or dividing by miles.</p>
<p>So x miles/ (miles/hour) + x miles / (miles/hour) = hour. That is true.</p>
<p>So x miles / 45mph + x miles/30mph = 1 hour. Solve for x. And you get x = 18. So she drove 18 miles to work.</p>
<p>EDIT: My answer seems a little esoteric. Here is a link to various other solutions for this question.
<a href="http://talk.collegeconfidential.com/sat-act-tests-test-preparation/74410-hard-math-problem.html%5B/url%5D">http://talk.collegeconfidential.com/sat-act-tests-test-preparation/74410-hard-math-problem.html</a></p>
<p>SAT loves this type of problem easy formula:</p>
<p>speed 1 = Z
speed 2 = Y</p>
<p>(Z * Y)/(Z + Y)</p>
<p>(45 * 30)/(45 + 30)</p>
<p>1350/75 = 18</p>
<p>For round trip problems multiply by two</p>
<p>ok the quickest way is 45mph-30mph=15mph, but she used an hour, so add 3, so it's 18 miles to work</p>
<p>all you have to know is that:</p>
<p>Distance= rate x time</p>
<p>for example,</p>
<p>18 miles = 1 mph x 18 hours</p>
<p>why are we adding 3.. based on what logic? O_o</p>