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February 7th, 2017, 05:48 AM  #1 
Member Joined: Aug 2016 From: South Korea Posts: 55 Thanks: 0  Application in real life of Derivatives
A train starting @noon, travels north at 40m/hr. Another train, starting from the same point @2pm travels east at 50m/hr. Find to the nearest mile/hr how fast the train are separating @3pm. How should I do this? please explain to me of how or what should I do to answer this? ㅠㅠ 
February 7th, 2017, 06:04 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
Set up equations, let $t=0$ be noon and the starting position at the origin. Train #1 ... $y = 40t$ Train #2 ... $x = 50(t2)$ Distance between the two is $s=\sqrt{x^2+y^2}$ Determine the value of $\dfrac{ds}{dt}$ at time $t=3$ 
February 7th, 2017, 06:59 AM  #3 
Member Joined: Aug 2016 From: South Korea Posts: 55 Thanks: 0 
Should I use Pythagorean for finding ds/dt?

February 7th, 2017, 07:10 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600  Pythagoras was used to find $s = \sqrt{x^2+y^2}$. The difficult part is done ... it's all set up for you. you have two ways to go with this ... 1. take the implicit derivative w/r to time, i.e. $\displaystyle \frac{d}{dt}\left(s = \sqrt{x^2+y^2}\right)$ 2. take the explicit derivative w/r to time ... $\displaystyle \frac{d}{dt}\left(s = \sqrt{[50(t2)]^2+(40t)^2}\right)$ Remember that you're finding the value of $\displaystyle \frac{ds}{dt}$ at $t=3$, which also means you'll need the values of $x$ and $y$ at that time also if you go the implicit route. Do not substitute values in until after you find the derivative. Last edited by skipjack; April 23rd, 2019 at 11:23 PM. 
February 7th, 2017, 07:13 AM  #5 
Member Joined: Aug 2016 From: South Korea Posts: 55 Thanks: 0 
Oh~ Thanks a lot! ^^

April 17th, 2019, 07:41 PM  #6 
Newbie Joined: Apr 2019 From: Philippines Posts: 1 Thanks: 0 Math Focus: Algebra 
Hello, can you help me show the solution of this problem, please?
Last edited by skipjack; April 23rd, 2019 at 11:22 PM. 
April 18th, 2019, 03:56 AM  #7 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600  What have you tried to determine $\displaystyle \frac{ds}{dt}$ at the specified time?
Last edited by skipjack; April 23rd, 2019 at 11:22 PM. 
April 23rd, 2019, 04:54 PM  #8 
Member Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 
I always find the explicit form bad practice. It’s a related rate. Set up the total differential then take the derivative with respect to time. However, the OP struggled with the explicit case and absconded when no solution was given.

April 24th, 2019, 07:19 AM  #9  
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600  Quote:
To say one method is "always" bad practice is rather presumptuous, don't you think? Sometimes, using both explicit & implicit methods helps to confirm a solution.  
April 25th, 2019, 03:46 PM  #10 
Member Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 
I wouldn't say bad practice; I'd consider it a habit for the less able. A lot of knowledge can be expressed implicitly in a statement two inches in length.


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