<p>In preparing for a race, Jill ran 1/2 the distance that Sam ran, and Sam ran 3 times the distance that Aisha ran. What was the ratio of the distance that Jill ran to the distance that Aisha ran?</p>
<p>A. 1 to 3
B. 1 to 2
C. 2 to 3
D. 3 to 2
E. 5 to 1</p>
<p>Here's how I attacked it:
J=(1/2)S
S=3A
J=(3/2)A
2J=3A
2 to 3 ratio</p>
<p>What's wrong with my method and why is it giving me the wrong answer?
How do you guys solve something like this?</p>
<p>Thanks ^_^</p>
<p>I didn’t really approach this like you did (so this may not be what you are looking for), I just plugged in numbers that fit. Pick a number that is divisible by both 3 and 2, and that’s Sam. Divide that number by 2 and that’s Jill/by 3 and that’s Aisha.</p>
<ol>
<li>Jill = 3, Sam = 6, Aisha = 2</li>
</ol>
<p>Jill : Aisha = 3:2 </p>
<p>So I would say D</p>
<p>Use the plugin method</p>
<p>Jill runs 6 miles, so Sam runs 12. If Sam runs 3 times as much as Aisha, then Aisha ran 4 miles.</p>
<p>6 miles to 4 miles= 3:2 ratio</p>
<p>Edit: Beat me ^^</p>
<p>You did practically everything correct. The spot where you made your mistake was at the very end:
“2J=3A
2 to 3 ratio”</p>
<p>Thing about what this means. Simplify it even further. </p>
<p>J=(1.5)A</p>
<p>^^ J=(1.5)A means that the distance Jill ran was equal to the one and a half times the distance that Aisha ran.</p>
<p>So, Jill ran more than Aisha.</p>
<p>Just plug in numbers now like Vince011 did.</p>
<p>J=(1.5)A</p>
<p>3=(1.5)2</p>
<p>3=3</p>
<p>So, if you plug in 3 for Jill and 2 for Aisha, the equation works. So the correct answer is: </p>
<p>D. 3 to 2</p>
<p>Pwnstar, your work is correct, but you probably misread the question.</p>
<p>The question asked for J to A, so instead of your 2:3(A to J), it’s 3:2.</p>
<p>J/A = 3/2</p>