Thread: Word problem involving perpendicular lines

You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 39 km south and 222 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?

______ minutes

So I worked it out and thought it would be 16 minutes, but I was wrong. Can someone help me?

Hey DasRabbit.

Can you show us how you got the 16 minutes? Doing this will aid us in understanding your thought process and this is a lot more effective than us guessing on your behalf.

39x + 222y = 0
13x + 74y = 0


74x - 13y = c ... is the perpendicular line
74x - 13y - c = 0

(56, -40) is
.. 74x - 13y - (74(56) - 13(-40)) = 0
.. 74x - 13y - 4664 = 0
The distance is
.. |74(0) - 13(0) - 4664|/√(74^2+13^2) = 4664/√5645 = 62.076

62.076 km in 62.076/800 hr = 4 min 39 sec

Time is 16 minutes, 54 seconds.