Fastest way to solve this? distance problem

Test Preparation SAT Preparation
1

<p>Jennifer ran from her house to school at an average speed of 6 miles per hour and returned along the same route at an average speed of 4 miles per hour. If the total time it took her to run to the school and back was one hour, how many minutes did it take her to run from her house to school?</p>

<p>The way I did it:
d=rt
d=6t</p>

<p>6t = 4(1-t)
t = 4/10 * 60
t = 24 minutes</p>

<p>also, which problems can you use xiggi's average rate formula (2<em>speed1</em>speed2)/(speed1+speed2)? Can you use it for this one?</p>

<p>Thanks! ^^</p>

2

<p>You can use that formula when the distance is the same for each speed, which is the case here. </p>

<p>r=(2<em>4</em>6)/(4+6)=4.8 mph</p>

<p>d=rt=(4.8)(1)=4.8 miles (divide this by two to get one leg of the trip)</p>

<p>t=d/r=2.4/6=.4 hours=24 minutes</p>

3

<p>TortoroMan-
Your method took only 3 simple lines of algebra and you’re looking for an EASIER way???
I think your approach is best. Xiggi’s average rate formula doesn’t save any time at all on this one. Compare your “work” to Silverturtle’s.</p>

<p>In addition, your approach is more broadly applicable to many types of problems whereas the special formulas with limited applicability only work in very specific circumstances and often get used in inappropriatey.</p>

<p>Often in T,D,S problems, one of the 3 is equal; here it’s the distance. Just set the 2 things that are the same equal to one another like you did. Then replace the terms with their formulas ST, D/S or D/T.</p>

4

<p>can you link me to silverturtle’s “work”, I can’t seem to find it :(</p>

5

<p>Its the second post in this thread</p>

6

<p>OP, your solution is straightforward, quick, correct, and extensible to related situations in which a memorized formula would not apply; i.e., OhhhYouKnow nailed it.</p>

7

<p>The other methods are correct and are applicable to harder math questions, but in this problem where distance is irrelevant this could/should be the quickest method.</p>

<p>

</p>

<p>Total Time = 60 minutes
Home -> School = 6 mph
School -> home = 4 mph</p>

<p>Solve for t:
4t + 6t = 60<br>
10t = 60
t = 6</p>

<p>Plug in t
6 * 4 = 24</p>

<p>Check:
4<em>6 = 24
6</em>6 = 36
24 + 36 = 60</p>

8

<p>ok guys thanks, I was just wondering that’s all, so you do need to be flexible with solutions, formulas etc. :)</p>