Question 777892: Radar detected on unidentified plane 5000 mi away, approaching at 700 mi/h. Fifteen minutes later an interceptor plane was dispatched, traveling at 800 mi/h. How long did it take the interceptor plane to reach the approaching plane?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Radar detected on unidentified plane 5000 mi away, approaching at 700 mi/h. Fifteen minutes later an interceptor plane was dispatched, traveling at 800 mi/h. How long did it take the interceptor plane to reach the approaching plane?
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We are dealing in mph, change 15 min to .25 hrs
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Let t = time for the interceptor to engage the target aircraft
then
(t+.25) = travel time of the target
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The distances traveled by the two aircraft at interception will equal 5000 mi
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Write a distance equation; dist = speed * time
800t + 700(t+.25) = 5000
800t + 700t + 175 = 5000
1500t = 5000 - 175
t = 4825/1500
t = 3.2167 hr or 3 + .267(60) = 3 hr 13 min to intercept
:
:
Check this by finding the travel distance of each a/c
800 * 3.2167 = 2573 mi\
700 * 3.4667 = 2427 mi
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total dist: 5000 mi
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