SOLUTION: 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 650 mile

Question 154274: 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 650 miles apart?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 650 miles apart?
-------------------
Draw the picture on a coordinate system; use the y-axis for north
and the x-axis for east.
---------------------------
Let the time in hours be "x" for both planes
North distance = 500x miles
East distance = 1200x miles
-------------------------------
Use Pytagoras with a hypotenuse of 650 miles.
EQUATION:
(500x)^2 + (1200x)^2 = 650^2
250000x^2 + 1440000x^2 = 650^2
1690000x^2 = 650^2
x^2 = 0.25
x = 0.5 hours
------------------
Time = 30 minutes
========================
Cheers,
Stan H.
RELATED QUESTIONS
An airplane leaves Los Angeles for Denver at a speed of 430 mph. Thirty minutes later, a... (answered by mananth)

A plane flies from Colorado Springs due north to Denver, a distance of 70 miles. Due to... (answered by ankor@dixie-net.com)

Marty leaves the airport in his private plane and flies due east at 186 mph. Two hours... (answered by checkley71)

Marty leaves the airport in his private plane and flies due east at 186 mph. Two hours... (answered by stanbon)

an airplane A leaves los angeles for denver at a speed of 450 mph. thirty minutes later a (answered by stanbon)

An airplane leaves Los Angeles for Denver at a speed of 410 miles per hour (mph). Thirty (answered by drglass)

an airplane leaves Los angeles from denver at a speed of 410 mph. thirty minutes later a... (answered by macston)

An airplane is heading due north at 260 mph. a 16 mph window blows from the east. what is (answered by ankor@dixie-net.com)

At noon a train leaves cleveland and heads due north at 10 mph. Another train leaves at... (answered by Fombitz)