<p>A man rode a bike a straight distance at a speed of 10 miles/ hr and came back the same distance at a speed of 20 miles/hr. What was the mans' total number of miles for the trip back and forth if his total traveling time was 1 hr?</p>
<p>My question is why can't we add 10+20 up and find that distance</p>
<p>You can’t add them up because they are different speeds. You need to find out the amount of time that he was traveling at each speed.</p>
<p>10/(10 + 20) = 1/3h
20/(10+ 20) = 2/3h</p>
<p>So he spent 1/3 of an hour at 20mph and 2/3 of an hour at 10mph.</p>
<p>So the distance is 1/3h x 20mph = 6 2/3m</p>
<p>Don’t forget to multiply by 2 since the question asks for total distance.</p>
<p>The answer is 13 1/3 miles.</p>
<p>2x10x20/(10+20) = 13 1/3</p>
<p>housecat, for 10/(10 + 20) = 1/3h
what formula did you use?</p>
<p>I didn’t really use a formula (I took the SAT two years ago). I just found out what percentage of the hour that the man spent at each speed.</p>
<p>Since you have 1/3 hour, you know that the man must have been traveling 20mph for 1/3 hour because he obviously spent less time traveling 20mph than he spent traveling 10mph.</p>
<p>Multiply time x speed to get the distance (hours cancel out).</p>
<p>1/3h x 20mph = 6 2/3</p>
<p>Then multiply by two since it is a round trip.</p>
<p>Or, if you like using algebra…</p>
<p>Call the distance each way d. The time each way is the distance over the speed. And it adds up to 1 hour. That gives you:</p>
<p>d/10 + d/20 = 1</p>
<p>Which you can solve for d…but then you have to double it to get the round trip distance.</p>
<p>As for how to solve the equation: lazy kid uses ti89.</p>
<p>For those who scorn such laziness, multiply both sides through by 20. You get</p>
<p>2d + d = 20</p>
<p>3d = 20</p>
<p>d=20/3. But again, you have to double that.</p>
<p>xiggi’s formula, used by gfc, is really the fastest way. </p>
<p>2(R1)(R2) / (R1+R2)</p>