<ul>
<li>A woman drove to work at an average speed of 40 miles per hour and returned along the same route at 30 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?</li>
</ul>
<p>There's some rule, an algebraic one that is, like 40x + 30x or something like that. Can anyone kindly elaborate?</p>
<p>There’s a faster formula that’s shared in this forum but the one I use is the basic way.</p>
<p>You know that D=RT, that is: distance equal rate x time</p>
<p>so that means that time is distance/rate</p>
<p>The distance for each trip is the same because it’s the same route both ways. we are also trying to find the distance so lets call it x. The rates are 40 are 30. So the time of the first trip is x/40. and the time of the second trip is x/30. you know the total time is 1 hour. </p>
<p>then x/40 + x/30 = 1 (hour)</p>
<p>solve that to get the distance :)</p>
<p>try this and see if you get the correct answer!</p>
<p>ps. remember the answer is 2x —> “total number of miles in the round trip”</p>
<p>Since this is a grid in, there are no choices to help us. </p>
<p>I will give two ways to solve it.</p>
<p>Method 1: Make little chart:</p>
<p>d=r*t
d 40 d/40
d 30 d/30
2d ? 1</p>
<p>So d/40 + d/30 = 1
30d+40d =(30)(40)
70d=(30)(40)
2d=(30)(40)/70 = 34.2 (truncated)</p>
<p>Method 2: If you know Xiggi’s formula you can use it here.</p>
<p>r=2(r1)(r2)/(r1+r2)=2(30)(40)/70 = 34.2 (truncated).</p>
<p>So d=r<em>t=34.2</em>1=34.2</p>
<p>Note: r is the average rate for the whole round trip, t is the total time, and d is the total round trip distance (this is different from the solution above).</p>
<p>Important Note: Xiggi’s formula does NOT give the distance here. It gives the RATE. The 2 numbers are only the same because the total time is 1. If the total time were 5, for example, you would have to multiply the rate (the number you get from Xiggi’s formula) by 5.</p>
<p>Thank you both so much! :-)</p>