<p>Bernardo drives to work at an average speed of 50 miles per hour and returns along the same route at an average speed of 25 miles per hour. If his total travel time is 3 hours, what is the total number of miles in the round-trip?</p>
<p>a) 225
b) 112.5
c) 100
d) 62.5
e) 50</p>
<p>Why is the answer C</p>
<p>Here are the ways I did it when I encountered this question
<p>Goes like that (2<em>50</em>25)/(50+25)*3 = 2500/75= 100/3 * 3 = 100
if you remember that formula its probably the fastest.
(It can be found on Xiggi’s thread)
Another option is that: the round trip couldn’t take 50 or 62.5 because even if he drove the entire 3 hours on 25MPH it would be 75, it also can’t be 225 because if he drove for 3 hours on 50MPH it would get only to 150.
Now lets check b: if the trip is 112.5MPH that means he did 56.26 miles each way, so the way to work took him a bit over an hour and the way back took him a bit over 2 hours, now thath’s more than 3 hours so it’s no good.
Just to be sure lets look at C: that means 50 miles to work and 50 miles back, so the way to work took 1 hour and the way back took 2 hours, thath’s exactly 3 so that works.</p>
<p>Hope it helped :)</p>
<p>Can you explain when you would use xiggis method?
Sent from my SCH-I535 using CC</p>
<p>You can also exploit a lil symmetry with this one…</p>
<p>If he went 50mph there and 25mph back, it took him twice as long to go back as it did to go there. If his total time was 3 hours, it must have taken him 1 hr there, 2 hrs back. 1 hr x 50mph + 2 hrs x 25mph = 100 miles</p>
<p>Average speed is just distance divided by time, so set the distance as “d” and time as “t” </p>
<p>For the trip there: d/t= 50
For the trip back: d/(3-t) = 25 <---- Since total time is 3 hours, if it took “t” time to get to work, it’ll take “3-t” time to get back; the distance remains the same. </p>
<p>If you multiply so only “d” is on both sides, you get: </p>
<p>d= 50t and<br>
d= 75 -25t</p>
<p>Set them equal to eachother: </p>
<p>50t= 75-25t
75t = 75
t= 1</p>
<p>This means that it takes 1 hour to get to work. If you put t=1 back into your first equation (d=50t), you find that d=50. Since you’re asked to find the total in the round trip, multiply 50 by 2, and you get 100.</p>
<p>Xiggi’s formula can be used to find average speed when 2 individual speeds for the SAME distance are known. </p>
<p>The answer you get will be the average speed for the ENTIRE distance travelled.</p>