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March 14th, 2019, 01:30 PM   #1
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Total time problem

First worker capacity alone to do the work : 12 hours
Second worker capacity alone to do the work : 6 hours
They start working together for 3 hours and then the second worker continues to work alone .
How much time the second worker did work ?

Last edited by idontknow; March 14th, 2019 at 02:05 PM.
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March 14th, 2019, 02:16 PM   #2
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March 14th, 2019, 02:25 PM   #3
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Quote:
Originally Posted by idontknow View Post
First worker capacity alone to do the work : 12 hours
Second worker capacity alone to do the work : 6 hours
They start working together for 3 hours and then the second worker continues to work alone .
How much time the second worker did work ?
$t$ is number of hours worker 2 worked alone

$3\left(\dfrac{1}{12} + \dfrac{1}{6} \right) + t \cdot \dfrac{1}{6} = 1$
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March 14th, 2019, 03:03 PM   #4
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To "see" it clearly, make up something simple, like:
make "the work" = travelling 120 miles;
1st driver's speed = 10 mph, 2nd driver's speed = 20 mph:

@(20+10)mph.......90m........>3hr@20mph....30m.... ..>1.5hr

Clear?
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