<p>I'm having trouble with this Cambridge bk math question, #23, pg. 489. Any help would be really appreciated. :)</p>
<p>Peter walked from point P to point Q and back again, a total distance of 2 miles. If he averaged 4 miles per hour on the trip from P to Q and 5 miles per hour on the return trip, what was his average walking speed for the entire trip?</p>
<p>A. 2 and 2/9
B. 4
C. 4 and 4/9
D. 4 and 1/2
E. 5</p>
<ol>
<li>The formula 2(rate1)(rate2)/(rate1 + rate2) gives the average of two rates when a person travels X distance at rate1 and X distance at rate2.</li>
</ol>
<p>2(4)(5)/(4+5)
= 40/9
= 4 4/9</p>
<ol>
<li>Think before you solve. This is a weighted average problem. He would have walked for a longer period of time at 4 mph than at 5 mph because at the slower rate, he would need more time to cover the same distance. So the answer is going to be slightly under the straight up average of the two rates (4.5) . Answer D is the trap and the straight average of the two rates, so the choice right below it in value is correct, C (4.4444…)</li>
</ol>