Wind and Current Problems | MathHelp.com - By American English
Transcript
| 00:0-1 | into a headwind . The plane flew 2000 miles in | |
| 00:04 | five hours with a tail wind . The return trip | |
| 00:08 | took four hours . Find the speed of the plane | |
| 00:11 | and still air and the speed of the wind . | |
| 00:16 | Let's start things off by setting up a chart based | |
| 00:20 | on the formula rate times , time equals distance for | |
| 00:24 | the two trips that are plane took into a headwind | |
| 00:29 | and with a tail wind , if we use the | |
| 00:33 | variable P . To represent the speed of the plane | |
| 00:43 | and w . To represent the speed of the wind | |
| 00:51 | , then remember from the previous example that we can | |
| 00:54 | represent the speed of the plane into a headwind as | |
| 01:01 | P minus W . And the speed of the plane | |
| 01:08 | with a tail wind as P plus W . The | |
| 01:14 | time for the headwind trip is five hours And the | |
| 01:20 | time for the tailwind trip is four hours . So | |
| 01:25 | based on our formula rate times , time equals distance | |
| 01:29 | . The distance for our headwind trip Is five times | |
| 01:33 | print cease P -W . And the distance for our | |
| 01:38 | tailwind trip is four times sprint sees P plus W | |
| 01:46 | . Since we know the actual distance that the plane | |
| 01:49 | flies in each direction is 2000 miles . We can | |
| 01:55 | set each of our two distances equal to 2000 . | |
| 02:00 | So we have five times princes P -W equals 2000 | |
| 02:11 | and four times prints , sees P plus W equals | |
| 02:18 | 2000 . As our next step , I would divide | |
| 02:25 | both sides of the top equation by five . Mhm | |
| 02:33 | . To get P -W equals 400 and divide both | |
| 02:40 | sides of the bottom equation by four to get P | |
| 02:46 | plus W equals 500 . Now our system of equations | |
| 02:54 | is set up in a familiar way and we can | |
| 02:58 | use addition to solve it . Notice that when we | |
| 03:03 | add the two equations together , the Ws cancel And | |
| 03:07 | we have to p equals 900 To buy both sides | |
| 03:13 | by two , and p equals for 50 To find | |
| 03:21 | w . Plug 4 50 back in for P in | |
| 03:25 | either equation , and you'll find that W equals 50 | |
| 03:34 | so the speed of the plane is 450 mph , | |
| 03:45 | and the speed of the wind Is 50 mph . |
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