How to Solve Distance Rate Time Word Problems (D=RT)

[@myheavenx0180]

Thank you so much Miss Alyssa for making this video! I watched this video a few months ago and keep returning to it. I am homeschooled and this video explained how to solve D=rt better than any other videos I have seen.

[@YouCanLearnMathwithAlyssa]

Aw thank you so much! 😊

[@Artsport3535]

What homeschool program are u in

[@bassheadcolt]

Thank you so much! I love how you bring personality into how you present info.

[@YouCanLearnMathwithAlyssa]

Aw that’s so nice to hear - thank you! 😊

[@beth8589]

This is so helpful! Was stugglinh for like 1 week now, finding this vid was such a relief ugh😭 and the way u explained it make it so easy to understand! Thank you and subscirbing! :))

[@YouCanLearnMathwithAlyssa]

I’m so happy to hear it helped - and thank you so much for the kind words! 😊

[@chasewhitney3145]

Can you do more of these. And other problems like percentages change, and other basic math word problems. The way you teach is very helpful. Thank you

[@YouCanLearnMathwithAlyssa]

Aw thank you! I will definitely add those topics to the list 🙂. If you have a specific word problem in particular that you’d like an explanation for, please post it here and I’ll see about making a video of it! 😄

[@jin_cotl]

14:05 The last part was slightly confusing, the video says that they’re 200 miles apart and leave at 10am precisely. But the work showed the 45 and 55 mph, the new problem didn’t say that the cars traveled individually at 45 and 55. The new problem only stated that they’re 200 miles apart and both left at 10am.

[@caralarkin]

i'm going through algebra 1 on khan academy and i'm in this unit that is basically all different variations of your 2nd problem. I have really been struggling with it and i think my main problem has been not viewing (t-n) as a unit. so i would do 65 *t-1 instead of 65(t-1) and get 65t-1 instead of 65t-65. Its been very frustrating getting the wrong solution everytime. Usually it's some small issue that i'm struggling with like this. I hope this is helpful to someone else struggling with it. :)

[@YouCanLearnMathwithAlyssa]

That’s a great tip! It can be so frustrating when you’re soooo close to the answer but something small throws it out of whack. That’s awesome that you figured out what was going wrong and were able to correct it! 😊

[@ChatGPTofficialbot]

Math is great in the universe. And it shall be described in alyssa's way only. Thats the beauty of math

[@jin_cotl]

You’re incredibly self aware and I found your video to be quite helpful in understanding distance 😊

[@YouCanLearnMathwithAlyssa]

That is such a cool compliment - thank you! 😊

[@littlelemon3465]

Thank heavens for you Alyssa! Love your phone notification sound btw lol

[@YouCanLearnMathwithAlyssa]

Thanks 😂 - I’m glad I could help! 😊

[@slander4834]

alyssa you are a saint

[@YouCanLearnMathwithAlyssa]

Wow thank you! Glad to help 😊

[@nizamvula4064]

Just the video i was looking for, your teaching drama sounds makes it epic 😂😃😃,

[@brahmogamer3752]

This is really funny And is really helpful do ur thing Alyssa it is sad there is not many views this is soo helpful

[@YouCanLearnMathwithAlyssa]

Thank you so much! It really makes me happy to hear my videos are helping people 😊. I’ll keep making them, and hopefully more people will keep finding them 😄

[@Platinum989]

Thanks so much I live the way you explained everything

[@YouCanLearnMathwithAlyssa]

Thank you so much for the kind words - I’m so glad it helped! 😊

[@jin_cotl]

11:11 I think it’s 1:20pm instead of 12:20pm, because the second car didn’t move for an hour after the first car left. It took 4.33 hours to catch up after the second car started moving. The calculation only seemed to find how long it took for the car to reach the other car. It didn’t seem to include the wait time of one hour.

[@YouCanLearnMathwithAlyssa]

For this one there are actually TWO travel times. If you look at the chart, you’ll see that the time for the 50 mph car is “t” and the time for the 65 mph car is “t-1”. So when we solve for t, we’re solving for how long the 1st car traveled, which is 4.33 hours. The second car traveled for t-1 hours, or 3.33 hours. The first car leaves at 8 AM and travels for 4.33 hours, making it 12:20 PM. The second cars leaves one hour later at 9 AM and travels for 3.33 hours, which also makes it 12:20 PM. I hope I explained that in a way that makes sense - please let me know if you have any other questions! 😊

[@odishiengine4855]

I am listening 😊 the smile with reversing

[@iamliam1241]

Thank you so much.

[@YouCanLearnMathwithAlyssa]

You’re very welcome - I’m so glad it helped! 😊

[@daviddiaz-ly1ge]

thank you so much

[@YouCanLearnMathwithAlyssa]

You’re very welcome - please let me know if there are any other topics you need me to cover! 😊

[@bean481]

thank you i understand so much better this was so helpful you have a new subscriber :)

[@YouCanLearnMathwithAlyssa]

I’m so glad it helped - and thanks so much for subscribing! 😊

[@emoshoes333]

What about something like a truck driver is traveling at 65mph and gets distracted for 0.8 seconds, how far did he travel while distracted? It obviously involves converting, but I can't figure it out. Can you please help me out?

[@YouCanLearnMathwithAlyssa]

Sure 😊! The man is traveling 65 mph. We can write that as a fraction: 65 miles/1 hour. We want to know how far he travels in 0.8 seconds. Or, to put it as a fraction: x miles/0.8 seconds. To solve, we need to set these fractions equal to each other, but the units all have to be the same first. Right now, the “hours” and “seconds” don’t match. Personally, I would change the hours in “65 mph” to seconds. There are 60 minutes in an hour and 60 seconds in a minute. So 60 x 60 = 3600 seconds in an hour. Now we have our equation 65 miles /3600 sec = x miles / 0.8 sec Or just 65/3600 = x/0.8 To solve for x, we need to cross-multiply to get rid of the fractions. So 65 * 0.8 = 3600 * x Then 52 = 3600x Divide both sides by 3600, and you get x = 0.014444444… miles I’m guessing they probably want the answer in feet, so there’s one last conversion to do. There are 5,280 feet in a mile, so multiply that decimal by 5,280 and you get 76.2666… feet. Round to the decimal place they tell you to and you’re done 😁

[@zaferkhaliqi-y7q]

@@YouCanLearnMathwithAlyssa She asked and didn't thanked for your answer. I thank you instead🙏

[@HeyBigChriss]

Thank you. When I follow along with you, they are easy, however when im doing practice problems they are still hard for me to understand. Because on some you add and some you multiply. Could you explain how on some you chose to add and some you chose to multiply? I feel like I did a horrible job at explaining that. So, for example, on the second one, you set up an equation (50t + 65t - 65) but in the third one, you did not set up an equation, instead you just multipled, then subtracted that answer from the original? Idk how to know when or when not to set up an equation. Hope that made sense.

[@YouCanLearnMathwithAlyssa]

You’ve hit on what makes these problems so challenging for so many students - there are so many variations! 😱. The big difference between these two problems has to do with where the cars started versus where they ended. They also are asking us to solve for two different things, which adds another wrinkle. In the second problem, the cars both started at the same beginning point and stopped at the same destination, so they both drove the same distance. Since their distances were equal, and distance is the same as “rate x time”, we could set their “rate x times” equal to each other. That problem also is asking us to solve for the time it took them to get to that destination, so setting them equal to each other will help us solve for the variables and get that travel time. In the third problem, they end at the same destination, but they started at different beginning points. So, in that problem, they did not both travel the same distance to get to their destination. Which means we can’t set their “rate x times” equal to each other since their distance are not the same. Also, the problem is asking for the distance between their two beginning points. That means we need to figure out how far the first car traveled, how far the second car traveled, and then add them. Hope that helps! 😊

[@احمدغازيابوجياب]

Thank you so much ❤

[@YouCanLearnMathwithAlyssa]

You’re very welcome! 😊

[@badredboy188]

How bout when A bus leaves point A travelling at a speed of 30 mph. 20 minutes later a car leaves point A travelling in the same direction at 50 mph. At what distance will the car and the bus meet, and how much time will have elapsed?

[@YouCanLearnMathwithAlyssa]

This is going to play out just like the second problem in the video (time stamp is 7:54). In the example, the first car's rate is 50 and their time is t, while the second car's rate is 65 and their time is (t-1) since they leave 1 hour later and travel 1 hour less. You're going to set your problem up the same way, with one key difference. The bus will have a rate of 30 and a time of t. So far so good. The car will have a rate of 50... but a time of (t - 1/3). Why? Because we're in miles per HOUR and they gave you the start time in MINUTES. You have to change minutes to hours to make it work, and 20 minutes is one-third of an hour. From there, just solve as shown in the video 🙂

[@SATPrepTutoring]

Love the thumbnail haha

[@milkman9314]

I'm actually prepping for my asvab and I excelled st mathematics however when it comes to my arithmetic skills they're kinda bad so I'm back here 😅

[@YouCanLearnMathwithAlyssa]

If there’s any math topic that would help that I haven’t made a video for yet, please let me know 😊

[@ruthmatamoros5113]

Loved your video 😊

[@YouCanLearnMathwithAlyssa]

Thank you so much! 😊

[@crash7098]

So, how do you solve if you’re looking for speed? Driver A is going 15m/h faster than Driver B. If they pass each other at 11am, how fast was Driver A going?

[@YouCanLearnMathwithAlyssa]

If they’re starting from the same point and going the same direction, you’ll need to know what time they both started out before you can start solving. For example, if they tell you that the slower car left at 8 and the faster car left 15 minutes later, you would first make your d r t chart. Under t, you would have 180 (minutes) for the slower car and 165 for the faster car. The r for the slower car would be x, and x + 15 for the faster car. D=rt, so multiply the r and t columns together for each car to get your d for both of them. Now, they both traveled the same road, so their distances will be the same. Set your two “d’s” equal to each other and solved for x. Then use that x to get your speeds for the two cars.

[@crash7098]

@@YouCanLearnMathwithAlyssa I was on the right track with that. Perfect, thanks for the confirmation. 🙂

[@Cryptic_TM]

Yo Awesome Video but for the second question I am pretty sure you made a small mistake. Its not 4hrs 20 min. Im pretty sure its 3 hrs 20 min. When I checked the calculator the distance was different and it did not add up, can you help I am a little confused? Thanks

[@YouCanLearnMathwithAlyssa]

It’s both 4h20m and 3h20m, depending on which car we’re talking about😊. Here’s what I mean by that: when we solve for “t” in that problem, we get 4 hrs and 20 min. If you look at the original d=rt chart we made, “t” represents the time the 50 mph car traveled. It left at 8, then drove for 4 hr 20 min, stopping at 12:20pm. For the 65 mph car, the chart shows its time as “t - 1”. So its time was 4 hr 20 min minus 1 hour, or 3 hr 20 min. So it left 1 hour later than the first car at 9 am and drove for 3 hr 20 min until 12:20pm where it caught up with the 50 mph car. We can check that this is correct by multiplying 50 by 4 1/3 hrs to get number of miles driven and then multiplying 65 by 3 1/3 hrs to get its number of miles driven. You’ll get 216 2/3 miles for both. Hope that helps! 😊

[@Cryptic_TM]

@@YouCanLearnMathwithAlyssa ohhhh ok thanks a lot

[@Isaiahken]

My feed is so 😂😅❤😮😂😅🎉😊😂😅😂😮❤😮! Reply with emojis too!

[@odishiengine4855]

Lovely smile 😊❣️

[@shreknotfound]

this was a very helpful video!!! thank you, I hate these problems!

[@YouCanLearnMathwithAlyssa]

So glad it helped! 😄

[@xavy29]

same

[@jessiemcdaniel2474]

i don't understand at all how you build the problem to solve it still.

[@YouCanLearnMathwithAlyssa]

I’m sorry it wasn’t helpful 😥. Sometimes a one-on-one session can be a better option, since they can walk you through the specific problems you’re working on. I used to tutor on the Preply website - you can find great professional tutors there that can give one-on-one assistance. 😊

[@Jjjjjjj0007]

I just want the answer for a question in class 😊😅

[@Pixelpandas910]

you are so funny!

[@YouCanLearnMathwithAlyssa]

Aw thank you! 😊

[@theone-jm3gl]

You talk with too many fillers ..get to point

[@Terje-p8c]

Bro it’s math. Stop hating

[@jin_cotl]

Well teachers aren’t robots

[@larrymcbride79]

too much gab, bye.

[@hodansaidoffical]

Thanks you so much

[@YouCanLearnMathwithAlyssa]

You’re very welcome 😊