Question 29846: Hello! I am having problems with the following:
A commercial freight carrier is flying at a constant speed of 400miles/hour and is traveling 4 miles east for every 3 miles north. A private plane is observed to be 210miles due east of the commercial carrier, traveling 12miles north for every 5 miles west.
How fast is the private plane flying?
When will a collision take place if their paths are not averted?
I know this is a two system equation problem but I'm having problems setting up the equations? thank you so much!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Assume the commercial plane starts at the origin (0,0).
The slope of its path is 3/4, so it follows the line y=(3/4)x
The private plane starts at (210,0) and follows a line with
a slope of -5/12, so it follows the line y=(-5/12)x+(1050/12).
Find the intersection of these two lines.
I get (75,56.25)
Find the distance from the origin to the intersection point:
I get 93.75 miles.
Find the time it would take the commercial plane to fly that
distance; I get 0.2344 hrs.
Find the distance from (210,0) to the point of intersection:
I get 146.25 miles.
Find the speed the private plane must achieve to be able to
fly 146.25 miles in 0.2344 hrs.:
I get 623.93 mph.
I did this rather quickly so you had better check the figures.
Cheers,
Stan H.
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