<p>On a hike, Ian walked downhill 2/5 of the time and uphill 3/5 of the time. His downhill walking rate was 4 miles per hour, and his uphill walking rate was 2 miles per hour. The distance that Ian walked downhill was what fraction of the total distance that he walked?</p>
<p>A) 4/7
B) 3/7
C) 2/5
D) 2/7
E) 1/5</p>
<p>Thanks in advance!!</p>
<p>(4/5)<em>2=8/5 for downhill distance
(2/5)</em>3=6/5 for uphill distance</p>
<p>14/5=total distance</p>
<p>(8/5)/(14/5)=4/7 so A.</p>
<p>Hi Lauttuhella,</p>
<p>Thanks alot! Can you explain the working ? I don’t quite get how you derived the downhill and uphill distances…</p>
<p>I’m not completely sure if this is the right way, but I can try to help you with this. </p>
<p>Remember the equation, r*t = d
d=distance (m)
t=time (h)
r = rate (mph)</p>
<p>So, the distances are out of 5, and they speed is in mph. Multiply the denominators so that that they equal 60.</p>
<p>2/5 * 12/12 = 24/60 = Downhill Time
3/5 * 12/12 = 36/60 = Uphill Time</p>
<p>Now, multiply the number of minutes and the speeds to get the distances.</p>
<p>Downhill Distance = 24<em>4 = 96 m
Uphill Distance = 36</em>2 = 72 m
Combined Distance = 168 m</p>
<p>Then, you simply divide the downhill distance by the total distance, which is 96/168, or 4/7.</p>
<p>You could also multiply 2<em>4 = 8
3</em>2=6
8+6= 14</p>
<p>8/14= 4/7</p>
<p>Thanks alot everyone!</p>
<p>I got it now.</p>