Work Word Problems | MathHelp.com - By MathHelp.com
Transcript
| 00:0-1 | Macaulay can paint a house in 10 hours while it | |
| 00:03 | takes Clayton , 15 hours . If they work together | |
| 00:07 | , how long will it take them to paint the | |
| 00:09 | house ? To solve this kind of a problem , | |
| 00:13 | which is called a work problem . It's important to | |
| 00:17 | understand the following idea . Since macaulay can paint a | |
| 00:21 | house in 10 hours , we know that in one | |
| 00:24 | hour Macaulay can paint 1/10 of the house And in | |
| 00:29 | two hours Macaulay can paint 2/10 of the house . | |
| 00:33 | Therefore , in T Hours , Macaulay can paint T/10 | |
| 00:38 | of the house . And since it takes Clayton , | |
| 00:41 | 15 hours to paint the house in T hours , | |
| 00:45 | Clayton can paint t 15th of the house , pause | |
| 00:49 | the audio for a moment . If you need time | |
| 00:52 | to understand this idea . Now , to solve the | |
| 00:56 | problem , we use the following formula Part of job | |
| 01:00 | done by Macaulay plus part of job done by Clayton | |
| 01:04 | equals one job done . And were asked how long | |
| 01:08 | will it take them to paint the house ? So | |
| 01:11 | we're looking for the time or t . Remember that | |
| 01:15 | ? In t hours Macaulay can paint t tents of | |
| 01:19 | the house . So the part of the job done | |
| 01:21 | by Macaulay is T over 10 . And in T | |
| 01:26 | . Hours Clayton can paint t . 15th of the | |
| 01:28 | house . So the part of the job done by | |
| 01:31 | Clayton is T over 15 . Now we have the | |
| 01:35 | equation T 10th plus T 15th equals one . To | |
| 01:41 | solve this equation for T . We first get rid | |
| 01:44 | of the fractions by multiplying both sides of the equation | |
| 01:48 | by the common denominator of 10 and 15 , which | |
| 01:51 | is 30 , distributing on the left side , 30 | |
| 01:55 | times T over 10 is 30 T over 10 , | |
| 02:00 | Which simplifies to three T . and 30 times positive | |
| 02:05 | t . over 15 is positive 30 t over 15 | |
| 02:10 | , Which simplifies to positive two T . and on | |
| 02:13 | the right one times 30 is 30 , so we | |
| 02:18 | have three T plus two T equals 30 or five | |
| 02:22 | t equals 30 And dividing both sides by five T | |
| 02:27 | equals six . So if Clayton and Macaulay worked together | |
| 02:32 | , They can paint the house in six hours . | |
| 02:35 | Finally , it's a good idea to check your answer | |
| 02:39 | . If they worked together for six hours , then | |
| 02:42 | Macaulay paints 6/10 of the house and Clayton paints 6/15 | |
| 02:47 | of the house . So we have 6/10 plus 6/15 | |
| 02:52 | equals one . And reducing on the left side , | |
| 02:56 | we have 3/5 plus 2/5 equals one , which simplifies | |
| 03:02 | to 5/5 equals one , which is a true statement | |
| 03:06 | . So our answer checks . |
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