<ol>
<li><p>On a hike, Ian walked downhill 2/5 of the time and uphill 3/5 of the time. His downhill walking rate was 4mph, and his uphill rate was 2mph. The distance that Ian walked downhill was what fraction of the total distance that he walked?
(a) 4/7
(b) 3/7
(c) 2/5
(d) 2/7
(e) 1/5</p></li>
<li><p>The sum of the areas of three circles is pie. The radius of circle 2 is 1/2 the radius of circle 1, and the radius of circle 3 is 1/3 the radius of circle 1. What is the radius of circle 1.</p></li>
</ol>
<p>pick some time that he walked that is easy to work with, for example an 5 hours. So he walks 2 hours downhill and 3 hours uphill. so then u just pretty much plug in:</p>
<p>3 hrs (2miles/1hr) = 6 miles <—uphill</p>
<p>2 hrs (4miles/1hr) = 8 miles <—downhill</p>
<p>Ok so we know he goes a total of 14 miles right? Now just do 8/14 or 4/7</p>
<p>Oh sorry didnt’ see question 2, um so for number two define your radius for each circle</p>
<p>so circle 1: r = x
circle 2: r=.5x
circle 3: 4= (1/3)x</p>
<p>Ok with these variable radii, fine the area of each circle</p>
<p>circle1: (x^2)pi
circle 2 : (1/4)(x^2)pi
circle 3 : (1/9)(x^2)pi</p>
<p>So we know the sume of these areas is PI. So let’s add them. When adding fractions, find a common denominator, 36 is fine in this case.</p>
<p>so, ((36/36)(x^2)pi) + ((9/36)(x^2)(pi)) + ((4/36)(x^2)(pi)) = pi
which can be written as: ((49/36)(x^2)(pi)) = pi
So the pis can cancel out and we are left with: ((49/36)(x^2)) = 1
from here we know that x^2 = 36/49 or 6/7</p>
<p>So 6/7 is answer.</p>
<p>radius for circle 3 should not be 4=1/3x it should be r instead of 4…</p>
<p>Both answers are correct thanks a lot.</p>
<p>no prob dude, good luck</p>
<p>Nicework dipole. Is there an algebraic way of doing #1?</p>
<p>^ let (2/5)(4) represent the distance traveled downhill and (3/5)(2) represent uphill.
The total distance is the sum of these two distances.
(2/5)(4) = 8/5.
(3/5)(2) = 6/5.
8/5 + 6/5 = 14/5.
The question asks for the distance downhill out of the total distance, so
(8/5)/(14/5) = 8/14 = 4/7</p>
<p>An elegant solution, thanks!</p>
<p>let radius of circle 1 is 12k,then by question radius of circle 2 is 6k n of circle 3 is 4k
area of circe 1,2 and 3 is pi (12k)^2, pi (6k)^2 and pi (4k)^2 respecively
now by question
sum of radius is pi
therefore
pi (12k)^2 + pi (6k)^2 +pi (4k)^2=pi
pi((12k)^2 + (6k)^2 + (4k)^2)=pi
144k^2+36k^2+16k^2=1
k^2(196)=1
k^2=1/196
k=1/14
therefore radius of circle 1 is 12k=12/14=6/7</p>