Face Reveal! A problem with timing - can you solve this deceptive problem? - By tecmath
Transcript
| 00:0-1 | Get a welcome to tech mouth channel . I'm Josh | |
| 00:02 | , his little problem for you to solve . So | |
| 00:04 | we have a car and it's going over a hill | |
| 00:06 | here . So first it drives up the hill here | |
| 00:09 | and it has a distance of one mile that it | |
| 00:12 | has to go now . It's going pretty slowly . | |
| 00:14 | It's a bit of a clapped out old vehicle and | |
| 00:16 | it goes an average speed of 15 miles . Uh | |
| 00:20 | huh . Our Okay . So it gets to the | |
| 00:23 | top and now I can start going downhill and as | |
| 00:26 | you can imagine , you can probably got a little | |
| 00:28 | bit faster going downhill , right ? It has a | |
| 00:30 | distance also of one mile that it has to travel | |
| 00:34 | what speed would have to travel going downhill in order | |
| 00:37 | to have an average speed of 30 MPH for the | |
| 00:42 | entire journey . So pause the video . If you'd | |
| 00:45 | like to give this problem and try and when you're | |
| 00:47 | ready to keep watching , start up again . Time's | |
| 00:59 | up . How did you go ? The answer might | |
| 01:00 | not be exactly what you thought it was , especially | |
| 01:03 | if you didn't sit down and work it out . | |
| 01:04 | If you just tried to eyeball this one , I | |
| 01:06 | reckon you might have got in some difficulty , but | |
| 01:09 | let's go to the answer . But before we do | |
| 01:11 | that , what a lot to do is take this | |
| 01:12 | opportunity to mention the sponsor of this particular video . | |
| 01:16 | And that's white book . The best way to solve | |
| 01:18 | math problems is on a dry erase surface . And | |
| 01:20 | why is this ? It's because if you make a | |
| 01:22 | mistake you can erase it and keep going and let's | |
| 01:25 | face it with maths , you're gonna make plenty of | |
| 01:26 | mistakes . So check out this cost effective and interesting | |
| 01:30 | alternative . It's called a white book flip chart . | |
| 01:32 | It's a marriage between a conventional flip chart in the | |
| 01:35 | white board . So it comes with 20 surfaces per | |
| 01:38 | set , 10 double sided sheets . One side that's | |
| 01:41 | plain . And what's really handy , we have one | |
| 01:43 | side which is a graph side with graph paper which | |
| 01:46 | is really good for us , math people , what's | |
| 01:48 | also calls it integrates with the free white book scanner | |
| 01:51 | which is available on the app store or google play | |
| 01:54 | . So you can digitize and share your work by | |
| 01:56 | a google drive or any other popular cloud shared storage | |
| 02:00 | . You want to give white book flip chart to | |
| 02:01 | try check out www dot white book dot com slash | |
| 02:05 | tech . Math . I'll put the link in the | |
| 02:07 | description below and for a limited time you'll get 30% | |
| 02:10 | off your first purchase with white book . So check | |
| 02:14 | them out . So now let's get back to solving | |
| 02:16 | this particular problem here . Now , first off , | |
| 02:19 | there's a bit of an instinct that you might have | |
| 02:20 | if you just eyeballing this one and trying to work | |
| 02:22 | it out in your head where you just go OK | |
| 02:24 | . 15 plus what divided by two equals 30 and | |
| 02:28 | you might look at this in JK This unknown speed | |
| 02:31 | here is 45 mph . 15 plus 45 is equal | |
| 02:35 | to 60 divided by two is equal to 30 . | |
| 02:37 | But if you did that , you'd be wrong . | |
| 02:39 | So what we're going to do is we are going | |
| 02:41 | to use pen and paper or a white book if | |
| 02:44 | you've got one of those to work this out . | |
| 02:46 | So we're gonna be using speed calculations to do this | |
| 02:50 | as speed is equal to the following . So we're | |
| 02:52 | going to be using speed which is in MPH and | |
| 02:56 | this is equal to the distance , The distances in | |
| 03:00 | miles and this is divided by the time the time | |
| 03:04 | is in ours , but we're going to be using | |
| 03:06 | minutes . So we'll be converting as we go along | |
| 03:08 | here . So I'm just going to write that formula | |
| 03:10 | up here . That speed is equal to distance divided | |
| 03:14 | by time . But this is a problem with time | |
| 03:17 | . We're going to be working at times to get | |
| 03:19 | our answer . So I'm going to rearrange this particular | |
| 03:21 | formula here . So time is equal to distance divided | |
| 03:25 | by speed . So let's get rid of this particular | |
| 03:29 | formula down here and now we will start solving . | |
| 03:32 | So the very first thing we're going to do is | |
| 03:34 | we are going to work out the total time taken | |
| 03:37 | , so the total time taken to travel the entire | |
| 03:41 | uphill and downhill two miles . So this is going | |
| 03:44 | to be equal to the distance divided by the speed | |
| 03:48 | . Time equals distance divided by speed . And What | |
| 03:51 | will that equal ? Well , the distance , as | |
| 03:53 | you can see here , one mile up and one | |
| 03:55 | mile down . This is two miles . This is | |
| 03:58 | divided by the average speed that we're after . This | |
| 04:01 | 30 mph . So that's 30 there too , divided | |
| 04:04 | by 30 . This can be simplified to 1:15 . | |
| 04:09 | Now this is 1/15 of an hour . Now . | |
| 04:12 | What's that ? 10 minutes ? Well , there's 60 | |
| 04:14 | minutes in an hour . 1/15 of 60 . Well | |
| 04:18 | this is four minutes . So the total time that | |
| 04:22 | we have to travel uphill and downhill is four minutes | |
| 04:26 | . That's the first part . So the second thing | |
| 04:28 | where they are going to do is we're going to | |
| 04:29 | work at the time taken to travel up the hill | |
| 04:32 | here . So what's that going to be ? Let's | |
| 04:34 | call that the uphill time . So the uphill time | |
| 04:38 | is equal to the distance divided by the speed . | |
| 04:41 | So let's work this out . We have the distance | |
| 04:44 | which is one mile . We have a speed which | |
| 04:47 | is 15 MPH , so 1/15 , this is 1/15 | |
| 04:52 | of an hour , so what's that going to Eagle | |
| 04:55 | ? 1/15 of 60 . This is going to also | |
| 04:58 | equal four minutes . Now you may begin to see | |
| 05:02 | that we have a bit of a problem here , | |
| 05:04 | but let's not stop , let's just keep going okay | |
| 05:06 | and we will see this problem in a second . | |
| 05:09 | What we can now work out is the downhill time | |
| 05:11 | . So that's the last bit of time . We | |
| 05:13 | have to work out which is the downhill time . | |
| 05:16 | Okay , so what's that going to be ? Well | |
| 05:20 | we don't have to use distance over speed . Now | |
| 05:22 | what we can do is we can look at the | |
| 05:23 | total time To travel uphill and downhill which is four | |
| 05:26 | minutes . And the uphill time . The time taken | |
| 05:29 | to travel uphill which is four minutes and we can | |
| 05:31 | take one off the other . So the uphill time | |
| 05:34 | taken off the total time , four minutes , take | |
| 05:36 | away . Four minutes . You're going to see that | |
| 05:38 | we have zero minutes with which to now travel downhill | |
| 05:43 | . This entire trip here in order to have an | |
| 05:45 | average of 30 MPH you would have to do in | |
| 05:48 | zero minutes . As you can see . This question | |
| 05:53 | is a trick question . This can't be done . | |
| 05:55 | You can't travel one mile in zero minutes . Let's | |
| 05:58 | just apply the speed formula here just to prove that | |
| 06:01 | speed is equal to the distance divided by time . | |
| 06:04 | So we have the speed here . The speed you | |
| 06:07 | have to do the distance . Well that's one mile | |
| 06:10 | the time you have zero minutes in which to do | |
| 06:12 | this . Or zero minutes zero hours . One divided | |
| 06:15 | by zero . You know that life hasn't Very good | |
| 06:18 | when you try to go one divided by zero and | |
| 06:20 | it's not gonna work . I guess you could say | |
| 06:22 | maybe you need to be infinitely fast , but it's | |
| 06:25 | an impossible question . It's a trick question . It | |
| 06:28 | can't be done . Anyway , that's the solution to | |
| 06:31 | this . Hope you like this video and I hope | |
| 06:33 | you got that solution . Uh now look a big | |
| 06:36 | shout out to my patrons and a big shout out | |
| 06:38 | to my subscribers were at 995,000 subscribers were so close | |
| 06:44 | . Told me and subscribers I'm really , really quite | |
| 06:47 | excited and also a big shout out to the people | |
| 06:49 | of white book . I recommend to check them out | |
| 06:51 | . Once again , the link is in the description | |
| 06:53 | below . We have W W W dot white book | |
| 06:56 | dot com and make sure it's the dot com one | |
| 06:58 | . If you're outside Canada . These are a Canadian | |
| 07:00 | mob check him out anyway . Thank you and thank | |
| 07:04 | you for watching . See you next time . Bye | |
| 00:0-1 | . |
Summarizer
DESCRIPTION:
OVERVIEW:
Face Reveal! A problem with timing - can you solve this deceptive problem? is a free educational video by tecmath.
This page not only allows students and teachers view Face Reveal! A problem with timing - can you solve this deceptive problem? videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.
GRADES:
STANDARDS:
