<p>Hi guys,</p>
<p>I am working out some rate problems in order to master them,because I am not really good with rate problems. </p>
<p>These problems are from McGrawhills rate problems.</p>
<p>1)In three separate 1 mile races,Ellen finished with time of x minutes,y minutes,and z minutes. What was her average speed,in miles per hour,for all three races?</p>
<p>1)x + y + z /3
2)3 / x + y + z
3)x + y + z /180
4)180 / x + y + z
5)x + y + z / 20</p>
<p>In this problem what I don't get is that we are only given the time of minutes they finished,but we want Average speed which is distance/time,but we are only given time,so how we would suppose to solve this ? I don't understand its logic.</p>
<p>If x > 1,how many hours does it take a train traveling at x - 1 miles per hour to travel x^2 - 1 miles?</p>
<p>1) 1 / x -1
2) 1 / x + 1
3) x
4) x - 1
5)x + 1</p>
<p>Thanks in advanced.</p>
<p>im not completely sure about the first one, but the second one i would say E.</p>
<p>i just divided just x-1 by x^2 - 1 and all that was left was x+1</p>
<p>(1) I would definitely plug in numbers here. I’m running out the door right now and don’t have time to do it. If nobody gives details by tomorrow, then I’ll give a solution with specific numbers. I’ll also give an algebraic solution.</p>
<p>Thanks @ herozero1234 and DrSteve.</p>
<p>@Herozero
I want to know why though did you divide them out can you tell me the logic of why you did so?</p>
<p>Q1: Average speed = total distance / total time</p>
<p>total distance = 3 miles
total time = x+y+z minutes</p>
<p>Average speed = 3/(x+y+z) miles/minute but wait! The question asks for miles per HOUR.</p>
<p>x+y+z minutes * (1 hour / 60 minutes) = time in hours //notice how minute units cancel out</p>
<p>Average speed in mph = 3/((x+y+z)/60) = 180/(x+y+z) which is D</p>
<p>Q2: Distance = rate * time</p>
<p>therefore time = distance / rate</p>
<p>Rate = x - 1 mph
Distance = x^2 - 1 miles</p>
<p>Time = (x^2 - 1)/(x - 1)</p>
<p>By factoring the numerator you have ((x+1)*(x-1))/(x-1)
The (x-1)'s cancel out and you are left with (x+1) which is E</p>
<p>Hope this helps a little bit.</p>
<p>@Fantasma </p>
<p>I see now for question 2 I noticed the wording of the question I thought both were rate,so I was really confused,but now that makes perfect sense.</p>
<p>Thanks alot.</p>
<p>On sat one needs to read it really carefully :D.</p>
<p>fantasma beat me to it >.< haha but you understand it now.</p>
<p>I myself am not superb at rate problems but i used xiggi’s formula for many of them and it worked. I had to understand why it works and how to do them before i could properly solve them, but now it comes as a mediocre task. BUT there are still many rate problems i cant get such as the first one. working on em still</p>
<p>^Yeh me too I am doing some excerises on the internet hopefully 2 days I will master it,so I don’t miss it on the sat :).</p>
<p>Thanks anyway for your help and others aswell :).</p>
<p>no problemo! Im gonna start my ACT/SAT prep in a few days must clear all summer work first!</p>
<p>^Cool good luck with your SAT :).</p>