97% of people can not do this problem! Can you? - By tecmath
Transcript
| 00:0-1 | Welcome to the Tech Math Channel . I'm josh , | |
| 00:02 | consider this problem and see him . You can solve | |
| 00:04 | it . Allison Ben can do a job in three | |
| 00:07 | hours . Alison chris can do the same job in | |
| 00:10 | four hours . Ben and Chris can do the same | |
| 00:13 | job in six hours . So how long will the | |
| 00:16 | job take if they all work together ? So pause | |
| 00:18 | this video . If you'd like to give this problem | |
| 00:19 | and try and when you're ready to keep watching and | |
| 00:22 | learn how to solve this problem , started up again | |
| 00:33 | . Time's up and you try and solve this problem | |
| 00:36 | . Now , unfortunately , a lot of people are | |
| 00:38 | going to have got the incorrect answer for this and | |
| 00:40 | I'm going to show you why there's a tendency when | |
| 00:43 | we get this to turn these into algebraic equations . | |
| 00:45 | So Allison Ben , doing a job in three hours | |
| 00:48 | becomes a plus B is equal to three . Alison | |
| 00:53 | chris can do the same job in four hours and | |
| 00:55 | this becomes A plus C . Is equal to four | |
| 00:58 | . Ben and chris can do the same job in | |
| 01:01 | six hours to B plus C is equal to six | |
| 01:06 | . The next step is to want to put all | |
| 01:07 | these together and these are not bad steps so far | |
| 01:10 | . But there is a bit of a problem as | |
| 01:11 | you'll see . So first off we put all these | |
| 01:13 | together , we get the following we have a plus | |
| 01:16 | A . Is equal to two . A B plus | |
| 01:19 | B is equal to two . B . C plus | |
| 01:22 | C is equal to to see . And the sum | |
| 01:25 | of all these numbers on this side , three plus | |
| 01:28 | four plus six is equal to 13 to Alice is | |
| 01:32 | and two vans and two cruises all working together could | |
| 01:35 | get the job done in 13 hours . So now | |
| 01:37 | we can divide this whole equation by two and get | |
| 01:40 | what would seem to be our answer . So we | |
| 01:42 | end up with a plus B plus C is equal | |
| 01:47 | to half of 13.5 of 13 is 6.5 hours . | |
| 01:50 | And you might see a logical problem that we have | |
| 01:53 | here . It's taking these guys all working together longer | |
| 01:57 | than it is when they work separately . There's not | |
| 02:01 | a bit of logic , maybe that just says about | |
| 02:02 | how they work together , but anyway , we have | |
| 02:05 | a bit of a problem because it's how we've looked | |
| 02:06 | at the problem in the first place , the key | |
| 02:08 | is instead of trying to solve this problem by looking | |
| 02:10 | at how long it's taken to do the jobs instead | |
| 02:13 | , what we're going to do is we're going to | |
| 02:14 | look at how many jobs they can complete in a | |
| 02:17 | set amount of time . So let's do that . | |
| 02:20 | You got to solve this problem , we could just | |
| 02:21 | go through and see how much of these jobs these | |
| 02:24 | guys do within one hour and we end up with | |
| 02:26 | fractions Okay , these guys do a third of a | |
| 02:27 | job in an hour . These guys do a quarter | |
| 02:29 | of the job in one hour and these guys do | |
| 02:31 | 1/6 of the job in an hour , we can | |
| 02:33 | solve it that way . But instead of going to | |
| 02:34 | treat it a little bit differently just to make the | |
| 02:36 | numbers a bit easier . As you can see 3 | |
| 02:39 | , 4 and six are all common factors of 12 | |
| 02:42 | . So instead , what we're going to consider is | |
| 02:44 | how many jobs could these guys do within 12 hours | |
| 02:48 | ? So as you can see , Allison Ben could | |
| 02:50 | do four jobs , Alison Chris could do three jobs | |
| 02:54 | and Ben and Chris could do two jobs . So | |
| 02:57 | let's solve it now using these numbers here , so | |
| 03:00 | we end up with the algebraic equations , A plus | |
| 03:03 | B is equal to four , A plus C is | |
| 03:07 | equal to three , and B plus C is equal | |
| 03:12 | to two . Once again we're going to put all | |
| 03:14 | these together so we get the following to a plus | |
| 03:18 | two B plus to see . And this is going | |
| 03:22 | to equal the sum of all these numbers here . | |
| 03:24 | Now four plus three is equal to seven plus two | |
| 03:28 | is equal to nine . Once again we can have | |
| 03:31 | our answer here . So A plus B plus C | |
| 03:35 | is equal to half of nine , which is 4.5 | |
| 03:40 | . Now , this is not our end answer it's | |
| 03:41 | not 4.5 hours we're saying is in 12 hours working | |
| 03:45 | together these guys you get 4.5 jobs don't . So | |
| 03:49 | how long would it take them to get one job | |
| 03:51 | done ? Well simply we would just go 12 divided | |
| 03:55 | by 4.5 . So let's do that . And this | |
| 03:58 | will give us our and answer . Now if you're | |
| 04:00 | a terrible infractions you can just go 12 divided by | |
| 04:02 | 4.5 . But I think we're better than that . | |
| 04:05 | Let's use fractions to solve this . So we're going | |
| 04:08 | to end up with 12 divided by the improper fraction | |
| 04:12 | of nine over to which is equal to 12/1 . | |
| 04:17 | Multiplied by we do the reciprocal here to over 9 | |
| 04:22 | 12 times two is 24 divided by nine . So | |
| 04:27 | our answer is 24 divided by night . How much | |
| 04:29 | is that ? So 24 divided by nine . It's | |
| 04:33 | 2 to 9 to 18 and we end up with | |
| 04:36 | six left over 6/9 . This is equal to our | |
| 04:39 | final answer which is two and two third hours . | |
| 04:44 | Which if you want to be really damaging about it | |
| 04:46 | will be two hours and 40 minutes . So all | |
| 04:50 | these guys working together well , Honey , you slow | |
| 04:53 | . So how did you go with that ? Give | |
| 04:54 | you a lot of the problem ? Let us know | |
| 04:56 | in the comments below and people like button , please | |
| 04:59 | subscribe . I'm gonna be coming out with lots and | |
| 05:01 | lots more , uh , problems and maths and things | |
| 05:04 | like this . Anyway , thank you for watching . | |
| 05:06 | And we'll see you next time . Okay , well | |
| 05:08 | boy . |
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