# Tutor.com Linear Equations Session

##### Apr. 14, 2012

Session Transcript - Math - Algebra, 3/14/2012 8:25PM - Tutor.comSession Date: 3/14/2012 8:25PM
Length: 19.5 minute(s)
Subject: Math - Algebra

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Joshua (Customer)
[00:00:00] I need help on a Distance - Rate - Time word problem on a practise test that I am taking. I understand the formula's but I am lost on what to do if some of the parts are missing. The problem I am stuck on is as follows. A cargo plane flew to the maintenance facility and back. It took one hour less time to get there than it did to get back. The average speed on the trip there was 220 mph. The average speed on the way back was 200 mph. How many hours did the trip there take? I know Time = dis/rate but am unsure on what to do since dis is gone. I have an equation so far that looks like time for trip back = 200/x+1 time for trip there = 220/x That is where I get stuck at.

David Y (Tutor)
[00:00:25] Hello! Welcome to tutor.com ! Do you mind if I take couple of seconds to finish looking over this problem?

Joshua (Customer)
[00:00:40] Hello, of course

David Y (Tutor)
[00:00:55] Ok great! One moment...
[00:02:50] Ok great! So you are definitely on the right track!
[00:03:20] Let's start by taking our equation time=dis/rate:
[00:03:56] And so it is the distance that we have absolutely no information about, right?

Joshua (Customer)
[00:04:03] Correct

David Y (Tutor)
[00:04:48] Awesome! So let's actually solve this equation for distance rather than time. If we do that we would first multiply both sides by the rate, correct?
[00:05:28] Good so far?

Joshua (Customer)
[00:05:32] check

David Y (Tutor)
[00:06:14] Awesome! So let's start by writing the equation for the trip back. The average speed is 200 mph, so we plug that in for the rate:
[00:06:35] And how about the time. How would we write that?

Joshua (Customer)
[00:06:46] x+1

David Y (Tutor)
[00:07:00] You got it!
[00:07:27] Ok so let's do the trip there, now. For this trip, what is our average speed?

Joshua (Customer)
[00:07:47] 220 mph

David Y (Tutor)
[00:07:55] Awesome! And our time?

Joshua (Customer)
[00:08:00] so (220mph)(x)

David Y (Tutor)
[00:09:07] Ok awesome! So now here comes the key to this problem. Even though we arent given any information about the distance, we DO know that the distance there HAS to be the SAME as the distance back, right?

Joshua (Customer)
[00:09:18] correct

David Y (Tutor)
[00:09:41] Awesome! So that means that we can set these two distance equations equal, like this:
[00:10:10] Agreed?

Joshua (Customer)
[00:10:22] agree

David Y (Tutor)
[00:11:13] Awesome! And so now we have an equation where the only unknown is x. This means that we can solve for x! Do you have any thoughts as to how we might start that?

Joshua (Customer)
[00:11:46] Is this a proportion problem now?

David Y (Tutor)
[00:12:33] Not quite. We wont have to use proportions unless one or both of the sides have a denominator.
[00:12:58] So let's start by distributing the 200 through on the left side, like this:

Joshua (Customer)
[00:13:29] so 200x(200)?

David Y (Tutor)
[00:13:55] 200x times 200 or 200x + 200?

Joshua (Customer)
[00:14:02] check
[00:14:10] times

David Y (Tutor)
[00:15:23] Actually not quite, it will be plus. When we distribute, we want to multiply the 200 times the first and second term independently and then add or subtract depending on the sign here:
[00:15:36] So this would look like this:

Joshua (Customer)
[00:15:58] ok
[00:16:29] so then 200x + 200= 220x

David Y (Tutor)
[00:16:44] Ok awesome! You got it! Great job!

Joshua (Customer)
[00:16:47] then 440x=200?
[00:17:27] sorry
[00:17:33] 20x=200

David Y (Tutor)
[00:17:45] There you go! Excellent!

Joshua (Customer)
[00:17:44] then 200/20 x=10?
[00:18:21] ok, i understand now. Thanks for the help

David Y (Tutor)
[00:18:29] Awesome job! You got it!
[00:18:33] You are very welcome!
[00:18:41] Anything else before we bring this session to a close?

Joshua (Customer)
[00:18:52] I think that's it for now!

David Y (Tutor)
[00:19:01] Ok great!
[00:19:05] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â

Joshua (Customer)
[00:19:12] Will do

David Y (Tutor)
[00:19:18] Take care now! Awesome job with this problem! Have a great evening!
[00:19:20] Bye!