related rates

mr.burger

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Jun 12, 2005
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21
Two Trucks leave the same intersection one traveling East at 45 mph and the other traveling North at 60 mph. At what rate is the distance between them changing at 2 pm if they both leave at noon? If the north bound leaves at noon and east bound at 1 pm.?
 

Gene

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Oct 8, 2003
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The eastbound truck is at P(45t,0)
The northbound truck is at P(0,60t)
They form a right triangle so the distance between them is
D = sqrt((45t)^2+60t)^2)
find dD/dt at t=2

The eastbound truck is at P(45(t-1),0)
The northbound truck is at P(0,60t)
Same problem

I assume you needed help with the equations, not the derivitives.
 

mr.burger

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Jun 12, 2005
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21
is the answer to the first one 150 mph and the second one 128.2 mph????
 

Gene

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Nope, try again. You might show your work too. It can't possibly be more than 60+45. That would be if they were heading directly away from each other.
 

mr.burger

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Jun 12, 2005
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is the answer 1.4 mph and 12 mph??????????
 

Gene

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Nope. It is at least 60-45. That is the smallest it could be (if they were going the same direction.) Now you know 15<x<105.
You might show your work.
 
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