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Word problems - time, distance, rate

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by De Jan » Wed Jan 14, 2009 1:52 pm
I tried solve this question in a bit different manner and do not see where I am wrong. Here is the question:

An airplane leaves NY at 3pm and flies west at 200 mph. At 3:30pm another plane leaves NY and flies west as well, at 250 mph. At what time does the second plane overtakes the first?

The equation given as a solution was this:

200x=250(x-1/2)

x=the number of hours traveled by first plane
x-1/2 = the number of hours traveled by second plane

My question is: Why can't we have this equation in the form of:
200(x+1/2)=250x ???

(it still says that there is 30 min more to the time of the first plane, but does not give the same final result)

where:
x+1/2 = the number of hours traveled by first plane
x=the number of hours traveled by second plane

Thank you in advance!
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by hypik21 » Wed Jan 14, 2009 2:59 pm
here is how i did it..

by 3:30, the first plane is 100 miles into its journey

so at 3:30

100miles+(200x/mph)=250(x/mph)..x designates hours

50x=100miles
x=2 hours

2 hours after 3:30 is 5:30
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Time and Distance

by katz » Thu Jan 15, 2009 3:13 am
De Jan,

I am not going to comment on why your equation is correct or not. I would however, offer you an alternate view of solving problems of these types.

Here is my attempt. This problem could be solved very easily if you could fit as an equation of a line.

The equation of straight line is y = mx + c, where m = slope, and c = constant y intercept.

Plane one: since this plane has an head start of 30 minutes, it would have covered 100 miles before plane 2 gets started. The equation for plane 1 would therefore be: P1 = 200x+100

Plane two: the equation for this would be P2 = 250x

Now you are looking for a point where these two equations would meet.

So equate them and solve for x.
200x+100 = 250x
=> x = 2 hours (later).
Since P1 started at 3.30, the two planes would meet at 3.30+2 = 5.30 PM
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by mental » Thu Jan 15, 2009 6:15 am
My question is: Why can't we have this equation in the form of:
200(x+1/2)=250x ???
Both will yeild the same result

There seems to be small error in comparision. You might be comparing the value of x (rather than the final time) from both equations.

From 1st equation: x = 2.5hrs. Hence time = 3+2.5 = 5.5 = 5:30

From your equation: x = 2 hrs. Hence time = 3.5+2 = 5.5 = 5:30

Hope that clears the doubt
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Re: Word problems - time, distance, rate

by woo » Thu Jan 15, 2009 6:21 am
De Jan wrote:My question is: Why can't we have this equation in the form of:
200(x+1/2)=250x ???
Well.. Actually, you can!!

It is just that x in your equation is not same as the one in the other equation. Your x indicates the time taken by the plane 2 and x in the other equation is time taken by the plane 1. If you add the times to respective starting time you get 5:30 in both case

Plane 1 x=2.5=2:30
3:00+2:30=5:30
Plane 2 x=2=2:00
3:30+2:00=5:30
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by De Jan » Thu Jan 15, 2009 12:17 pm
Thank you all for the posts! Appreciate your time and help. I did not expect so many will reply so soon, as it is my first time on the blog but seems everyone is really helpful. Thank you!
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