My Math Forum Distance, rate, time problem

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January 12th, 2013, 01:28 PM   #11
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Re: Distance, rate, time problem

Quote:
 Originally Posted by jc90usa The problem reads: a plane flies 600 miles west (into the wind) and makes a return trip following the same flight path. The effect of the jet stream on the plane is 15mph. The round trip takes 9 hours. We want to find the speed of the plane in still air. In my problem i let $v=$the speed of the plane in still air
@v-15..........600...........>t

@v-15..........600...........>9-t

Results in two "different "t's" ...see that?
Agree that's it's confusing: a bit like the missing dollar riddle.

January 12th, 2013, 02:09 PM   #12
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Re: Distance, rate, time problem

Quote:
 @v-15..........600...........>t @v-15..........600...........>9-t Results in two "different "t's" ...see that? Agree that's it's confusing: a bit like the missing dollar riddle.
Thanks for letting me know about the missing dollar riddle, never heard of it.

So why do i need to plugin (v+15) into t, instead of (v-15)?

January 12th, 2013, 08:01 PM   #13
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Re: Distance, rate, time problem

Quote:
 Originally Posted by jc90usa I ask because I tried to make $\\ d_1=(v-15)(9-t) \\ d_2=(v+15)(t) ************(1) \\ d_1=d_2$ Once I get them to equal, I substituted t using t=d/r I am not sure why when I do this method I need to use $\\(1) t=\frac{600}{v+15}$ If I use, $\\ d_3=(v-15)(t) ************(2) \\ d_4=(v+15)(9-t) \\$ I need to use $\\(2) t=\frac{600}{v-15}$ to get the correct answer. Why does interchanging t for (9-t) affect it?
Well, my final attempt at trying to explain:
(1): the "t" here is the result of travelling 600 miles at speed v+15 ; t = 600 / 150 = 4
(2): the "t" here is the result of travelling 600 miles at speed v-15 ; t = 600 / 120 = 5

So the t in (1) is different from the t in (2). Good luck.

 January 12th, 2013, 11:26 PM #14 Newbie   Joined: Jan 2013 Posts: 13 Thanks: 0 Re: Distance, rate, time problem I got it!!! Thank you Denis and Mark, for your patience and explanations! After all your feedback and my working out problems in different ways, I understood what I was doing wrong. For anyone else having problems with these because they are asked to use a pesky table to represent d=rt, just remember that you are simply dealing with two rows of equations. First try to see if anything in the word problem points to "adding" the distances or the time. If it does, try using an addition equation. If anything in the word problem is equal, then you can try setting up an equality. IF you have to make substitutions, don't use the general d=rt and then reason what is required. (could work but prone to error, or ambiguity) USE either d=rt you created from the word problem to solve for the variable you need! The confusion is that the "addition" or "equality" method requires you to use d=rt generally to setup your addition or equality, but when substitution is required, a filled in d=rt is required. Being comfortable with those two, you should be able to handle if two unknowns are given. Happy day
 January 13th, 2013, 04:38 AM #15 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: Distance, rate, time problem Hey you can apply for your pilot's liscense now
 January 13th, 2013, 11:07 AM #16 Newbie   Joined: Jan 2013 Posts: 13 Thanks: 0 Re: Distance, rate, time problem hmmm m. that is an idea, lol

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# A plane flies 600 miles west into the wind and makes the return trip following the same flight path.

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