Who's up for two difficult math questions??

Test Preparation SAT Preparation
1

<p>Both have a difficulty rating of 5, beware. </p>

<p>First one: <a href="http://img686.imageshack.us/img686/2200/jan0820.jpg%5B/url%5D"&gt;http://img686.imageshack.us/img686/2200/jan0820.jpg&lt;/a&gt;&lt;/p>

<p>Second one: A car traveled 10 miles at an average speed of 20 miles per hour and then traveled the next 10 miles at an average speed of 40 miles per hour. What was the average speed, in miles, per hour, of the car for the 20 miles??</p>

<p>I used a formula for the second one and got the right answer, but is this the only way to do it? I used xiggi's method: (2<em>speed1</em>speed2)/(speed1+speed2)</p>

<p>Thanks! And I know the answers, I just need explanations. Thanks again!</p>

2

<p>For number 20:
Radius of large circle x4 = side of square</p>

<p>Side of square = 4</p>

<p>Now find the diagonal of the square via Pythagorean theorem:</p>

<p>sqrt(4^2 + 4^2) = sqrt(32) = 4sqrt(2)</p>

<p>Half the diagonal is 2sqrt(2).</p>

<p>2sqrt(2) - diameter of big circle = diameter of small circle</p>

<p>2sqrt(2) - 2 = diameter of small circle</p>

<p>we need radius of small circle so divide that by two</p>

<p>Answer is sqrt(2) - 1 or D</p>

<p>For the second one, xiggi’s method is the most reliable. Princeton R and Kaplan have other ways of tackling it, but they are longer and it boils down to the same thing.</p>

3

<p>Thanks a bunch! :)</p>

4

<p>Yeah for the second one you can use a harmonic mean (see wikipedia).</p>

5

<p>Second one:
The car traveled 10 miles at 20mph.
s = d/t
20 = 10/t
t was 1/2 hour</p>

<p>So 1/2 hour at 20mph.</p>

<p>s=d/t
40 = 10/t
t = 1/4 hour.</p>

<p>So 1/4 hour at 40 mph. </p>

<p>You could use the weighted average type thing or…</p>

<p>Total distance/total time = average speed</p>

<p>20 miles / 3/4 hour</p>

<p>= 26.7 mph</p>