How to do this Math SAT problem?

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1

<p>Calvin traveled from his home to another city at an average speed of 32 miles per hour, and then returned home along the same route at an average speed of 40 miles per hour.If his total traveling time for the trip was 3 hours, how many minutes did it take Calvin to drive from his home to the other city? hanks</p>

<p>I tried using the formula 2 * rate1 * rate2 / rate 1 + rate 2</p>

<p>But couldnt get the answer (assuming i did it wrong) .</p>

<p>Can anyone explain me how to solve the problem using that way?</p>

<p>Thanks</p>

2

<p>Is the answer 100 minutes?</p>

<p>If so, what I did was 32t=40(3-t)</p>

<p>the t you get is for the way there, if you want the way back do 3-t and then remember it should be in minutes.</p>

3

<p>I just solve these like this:</p>

<p>solve for distance by setting up this equation
x=distance from home to city
x/32 + x/40=3<br>
40x/1280 + 32x/1280=3 hours
72x/1280=3 hours
x=160/3</p>

<p>now just divide x by rate of travel there which is 32 and you get 5/3 hours</p>

<p>I am pretty sure thats right</p>

4

<p>nvm..........</p>

5

<p>"I tried using the formula 2 * rate1 * rate2 / rate 1 + rate 2"</p>

<p>^^ That formula is for average speed (or distance, when total time = 1 hr.)</p>

<p>You are looking for time to go one way (traveling at 32 mph), when total time = 3 hrs.</p>

6

<p>The answer is 100 minutes.</p>

<pre><code> (d) (r) (t)
</code></pre>

<p>Home to another city d 32 t</p>

<p>Another city to home d 40 3 - t</p>

<p>Total Total d Average Rate 3</p>

<p>You set up a table like this. Since the distances are the same, set both distances equal to d. Since total time is 3 hours, set Time 1 = t and that should make Time 2 = 3 - t. Then, run your d = rt for both home to another city and another city to home giving you the two equations: d = 32(t) and d = 40(3 - t). Since d = d, you can use transitive property to set 32(t) = 40(3 - t), then solve for t (t = 5/3). Since this is in hours and you want the answer in minutes, multiply 5/3 by 60 = 100 minutes. I hope that helps</p>

7

<p>The answer is 100 minutes.</p>

<p>This table is probably not going to come out right, but I hope you guys can figure it out. It's a 3 by 3 table with d, r, and t as columns and home to another city, another city to home, and total as the rows.</p>

<pre><code>distance (d) rate (r) time (t)
</code></pre>

<p>Home to another city d 32 t</p>

<p>Another city to home d 40 3 - t</p>

<p>Total Total distance Average Rate 3</p>

<p>You set up a table like this. Since the distances are the same, set both distances equal to d. Since total time is 3 hours, set Time 1 = t and that should make Time 2 = 3 - t. Then, run your d = rt for both home to another city and another city to home giving you the two equations: d = 32(t) and d = 40(3 - t). Since d = d, you can use transitive property to set 32(t) = 40(3 - t), then solve for t (t = 5/3). Since this is in hours and you want the answer in minutes, multiply 5/3 by 60 = 100 minutes. I hope that helps</p>