SM2 17.4.3 Finding Speed of a Current Given Distance and Total Time

Added: 2026-04-30

[00:00:01]Hello and welcome. So we have CJ here returning  from a trip to an event that was 2200 miles directly east of his home. Now when we're  talking about this we have 2200 miles to head to the place and another 2200 to head back.  All right. His total time for the entire flight both to and from his destination was 9 hours.  Now if the plane can go at 492 mph in still air how fast was the jet stream? Meaning that when  this plane is in the air it hits a jet stream, right? We're going to assume that this jet stream  is a constant speed. It's not going to be changing as well that it's the same one that CJ took to  the event as well as the same jet stream that they take back. Same flight plan. All right. So  when I'm looking at this I'd say all right well to relate these you're going to want distance equals  rate times time. Great way to relate anything in terms of rates with distances speeds and times. So  I like to make myself a table and figure out okay what do I know. So I know that we have the flight  to the destination and we have the flight from on our way back and then we also have some totals  here. Okay. And I'm going to say distance is my first column, rate the second, time the third. Now  I know the flight to it has a distance of 2200.

[00:01:30]I don't know how fast it was going because  assuming that the jet stream is aiding the plane it's going to be going faster than what it can do  without the jet stream. So it's going to be going faster than 492. It'll be whatever 492 is plus  the jet stream. Okay. Now I know nothing about the time because if it's going the round trip was  nine hours so it's going to be less than half is going to be on to the jet stream when it's aiding  it. Now the flight from we're going to assume is the opposite direction as our jet stream so it'll  be 492 minus the jet stream there. And then from there we're going to say all right don't know  that one but I do know that the total trip takes nine hours and I also know that technically it's  going to be 4400 for that. So I'd say okay what two columns do I know the most about? That's going  to be my distance and my rate. So what I'm going to do is I'm going to set up my equation for the  stuff I don't know which is my time. And I know it's going to be the time from trip to right and  it's going to be plus the time from the trip from our destination is going to be the trip... um... the time of the total. Okay. So how do we find that? Well use your relationship distance equals rate times time and just solve  for time, right? So we'd want to divide by the rate and we get distance over the rate equals the  time. Huzzah. All right. So we know the distance and the rate. We know the distance and the rate  for both of our trips and we also know the total time and that's going to work out really well when  we create this equation. So our time the flight of the trip to is going to be our distance over the  rate which I know is going to be 492 with my jet stream. All right. And then we're going to have  our trip from and that time is going to be the distance over the rate 492 minus the jet stream  equals the total time which we know is nine. And there you go. You know that you set this up  correctly and that you're going to be able to solve this because we have one variable in all of  this. It's just the j and that means that we can solve it. We have a relationship we have an equal  sign and there's only one variable. We're good to go. All right. Now there's a couple ways we can  solve this. I personally just like multiplying by my denominators to cancel out all of my fractions  because I know about you guys but I'm not a fan of fractions when I solve. So what I'm going to do is  I'm gonna kind of move these a little off to the side give myself some room to write. Is I'm going  to say all right this side I'm going to multiply by 492 plus the jet stream and 492 minus the jet  stream and do the same on the other side. 492 plus and 492 minus. So what's going to happen  that's over one so it distributes because you have addition and you're going to end  up with 2200 times (492 plus the jet stream) (492 minus the jet stream). I'm going to write  all of this out so you can see exactly why I'm doing what I'm doing. It's going to be kind of a  hassle to write but easier to see what happens.

[00:05:01]So we have 2200 times (492 plus jet stream) (492  minus jet stream) equals 9... whew, I'm running out of room, times (492 plus jet stream) (492 minus jet stream). Okay. Now the whole reason why we did that is because now you can notice this is all multiplication here meaning  that if you have the same thing top and bottom, boom, they can straight cancel out and that's exactly  what happens. So that means our 492 plus j gets canceled out the first fraction. Now we have just  2200 times (492 minus the jet stream) plus next fraction 492 minus jet stream because everything's  multiplication will cancel out 2200 times (492 plus j) equals 9 and then the other side  we just have our two parentheses (492 plus jet stream)(492 minus jet stream). Okay. And then  I prefer solving this because we don't have any more fractions now. Keep in mind you're going to  start noticing we have multiplication here. These numbers are going to be massive. They're going  to be huge and that's totally fine. All right.

[00:06:28]So we're going to do the first one 2200 times 492.  Okay so distribute to the first one get 1,082,400 minus 2200j plus same number as we distribute to  the first so 1,082,400 plus 2200j equals 9 times (492 squared is going to give us 242,064 and  that'll be 492 squared minus j squared). Those are going to cancel out and then minus j squared,  right? And then from there it's just a matter of combining your like terms. So minus and plus of  the same thing we're going to cancel on that one.

[00:07:26]Got that number. Combine these two together we get  2,164,800 equals over here we going to distribute that 9 through so 9 times 242,064 we get 2,178,576  minus 9j squared. Okay looks like a lot it is a lot honestly. So now it's just a matter of getting  your j alone. So I'm going to move the number over 2,178,576. Do what you do to one side do to  the other. Oops. 2,178,576 cancels and when you subtract those two together we're going to end up  at negative 13,776 equals 9j squared. Undo multiplication with division and you are so close at this point.  Um I'm going to move over to another calculator so you can see exactly what we're about to get.  So we're going to do our 13,776 divided by 9 and when we do you notice we're going to get a  decimal here. You do not want to round at this point okay because at this point this equals  j squared. Now remember as you're solving okay you're going to have j squared and say great how  do we undo a square? Square root. So when you take the square root what you do to one side you do to  the other. Technically you have plus minus here, right? So we're going to have plus minus the  square root of that number. I'm going to take the whole decimal with me so I don't round it too  early and we get positive 39.124and negative 39.124. All right. Now keep in mind we're talking about the speed of this  jet stream. Negative is not going to make sense, right? If someone asks you oh how fast are we  going on the freeway and you say negative 39 miles per hour it's not going to make sense,  right? So we only want the positive version of this. So 39.124 because we want third decimal  place. So we're going to say 39.124 and it says with units. Now our speed was in miles per hour  which means we should still be working in miles per hour. All right. You're welcome to use  mph or literally write out miles per hour.

[00:10:15]That will work. Just make sure there's no period  in there it's gonna freak out the code if you do.

[00:10:20]All right. So there you go. That is kind of your  solving on that one. A lot of writing a lot of big numbers it's totally fine. Just make sure you just  use calculator and crunch those. All right. But that is how you would solve this one or at least  one attempt for solving this. Thanks for watching.