<p>1.Graham walked to school at an avg speed of 3mph and jogged back on the same route at 5mph. If his total traveling time was 1 hour, what was the total number of miles in the round trip?
a. 3
b. 3 1/8
c. 3 3/4
d. 4
e. 5</p>
<p>Answer is C</p>
<p>Please help!</p>
<p>I’m sure there are multiple ways to do this, and I am not sure this is the easiest way, but here it is. You may have seen this formula discussed around the forum before, but you can find his AVERAGE speed for the whole trip by doing 2<em>3</em>5/3+5 which gives you 3.75 miles per hour for the trip. Since the trip is 1 hour, and you are going 3.75 miles per HOUR, you know the distance traveled is simply 3.75 miles and the answer is C. If the question asked for how long you were going in an hour and a half or something, you could have set up D=RT.</p>
<p>I still don’t really understand =( can you explain that 2x3x5/3+5 for me?</p>
<p>I’m not exactly sure why the formula works, but the formula 2<em>speed1</em>speed2/speed1+speed2 gives you the average speed of the entire trip. I am sure someone else can explain why this formula gives you the avg speed.</p>
<p>Distance divided by speed equals time, so</p>
<p>(distance) here is the round trip distance</p>
<p>(distance/2)/speed1 + (distance/2)/speed2 = time</p>
<p>We solve algebraically and get
((distance/2)<em>speed2 + (distance/2)</em>speed1)/(speed1<em>speed2) = time
distance/(2</em>time) = (speed1<em>speed2)/(speed1+speed2)
distance/time = (2</em>speed1*speed2)/(speed1+speed2)</p>
<p>That’s where that formula comes from.</p>
<p>I don’t really understand this part of the solving algebraically:</p>
<p>how u get from
(distance/2)/speed1 + (distance/2)/speed2 = time
to
((distance/2)<em>speed2 + (distance/2)</em>speed1)/(speed1*speed2)=time</p>
<p>Sorry I’m not really good at math but i think knowing how to do that would benefit me…</p>
<p>you start and stop at the same point so we he totaled zero miles in the entire trip. I took him t hours to get the the first point and 1-t hours to get back the original point. Rate x Time gives distance so we can set up an equation to explain this:</p>
<p>3(t)-5(1-t)=0</p>
<p>solving this we get t=5/8, meaning he walked at 3 mph for 5/8 of an hour and jogged 5 mph for 3/8 of an hour. since rate x time = distance we get 3(5/8)+5(3/8) = 3.75, or 3 and 3/4 miles.</p>
<p>if you memorize the formula you won’t have to understand how to use it. the answer isn’t 4 because the person spends more time going 3 mph than he does going 5 mph (because 3 mph is slower, so it takes more time). the average speed would only be 4 if he went 3 mph the same amount of time he went 5 mph. So since he spent more time going the slower 3 mph, the average speed has to be less than 4. the answer is C, 3 3/4 or 3.75 because going from 3 to 3.75 to going from 3.75 to 5 yields the ratio between the speeds.
so going from 3 to 3.75 is .75
going from 3.75 to 5 is 1.25</p>
<p>.75 : 1.25
3 : 5</p>
<p>these are equal ratios; .75/1.25 = 3/5</p>
<p>this is the concept behind the problem, no equation needed</p>
<p>I don’t really understand ratios that well, can u explain more?</p>
<p>you divide, .75/1.25 = 3/5</p>
<p>aa thx so much! I understand now crazybandit! You’re the best lol</p>