help me help my sis

T

thetomps

Junior Member
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Sep 26, 2005
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I'm tryint ot help my sister with this problem. Can anyone give us direction?

A plane leaves Denver heading due north at 500 mph. Simultaneously, another plane leaves Denver traveling due east at 1200 mph. After how many minutes will the planes be 325 miles apart?
 
that's a hard question. I guess it should be in calculus section.
I know how to find it, but by using diffferentiation. I dunno know whether it is right or not.
 
what answer do you get that way, kidz? I don't know how to find this one either? Should this person post this in calc or just leave it here?
 
Here is one approach, hopefully others will be posted.

Make a sketch.

You have a right triangle.

The hypotenuse is 325 miles.

Let the flight time in hours be, t.

After t hours the north bound plane has gone 500t miles and the east bound plane has gone 1200t miles.

When they are 325 miles apart you have a right triangle with a hypotenuse of 325 miles.


From Pythagoras' theorem you know.

(500 *t)^2 + (1200*t)^2 = 325^2

t^2(500^2 + 1200^2) = 325^2


Solve for t, multiply by 60 to get the minutes.

Ceck the distances in the triangle.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To set it up in minutes.

Let the flight time in minutes be, t.

Then after, t, minutes the north bound plane has gone (25/3)*t miles and the east bound plane has gone 20*t miles.

(25/3)^2 *t^2 + 20^2 *t^2 = 325^2

t^2 [(25/3)^2 + 20^2) = 325^2

Solve for t and check.
 
My post was confusing, I've edited it to try to tidy it up a bit.

Is your sister to work this all with or without a calculator.

t^2(500^2 + 1200^2) = 325^2

t^2 = 325^2/(500^2 + 1200^2)

t^2 = 1/16

t =

~~~~~~~~~~~~~~~~~~~~~

In minutes:


t^2 [(25/3)^2 + 20^2) = 325^2

t^2 (4225/9) = 325^2

t^2 = 325^2/(4225/9)

t^2 = [325/(65/3]^2

t = 325 * (3/65)

t = 975/65

t =

Can you find t, check the answers and let us know what distance each of the two planes is from Denver
 
Boy oh boy, fellas, why are you making this so difficult!

After 1 hour:
sqrt(500^2 + 1200^2) = 1300 miles apart

1300 miles = 60 minutes
1 mile = 60/1300 minutes
325 miles = 325 * 60/1300 = 15 minutes. Over and out!
 
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