Two missiles math puzzle
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4 members have voted
What is the ratio of the speed of missile A to missile B?
Quote: WizardTwo aircraft carriers fire missiles at each other at the same time (like in the movie The Spy Who Loved Me). However, the two missiles travel at different speeds, and do not hit each other in mid air. There is no wind and they follow the same trajectory, other than not hitting each other. After crossing each other, it takes 10 more minutes for missile A to reach its target. 90 minutes after the mid-air crossing, missile B reaches its target.
What is the ratio of the speed of missile A to missile B?
a * t = b * 90 because the distance traveled by missile A before mid-air crossing equals the distance traveled by missile B after mid-air crossing.
b * t = a * 10 because the distance traveled by missile B before mid-air crossing equals the distance traveled by missile A after mid-air crossing.
Solve each equation for t and equate: t = b * 90 / a = a * 10 / b.
Then a2 = 9 * b2; a = ±3 * b.
Quote: WizardTwo aircraft carriers fire missiles at each other at the same time (like in the movie The Spy Who Loved Me). However, the two missiles travel at different speeds, and do not hit each other in mid air. There is no wind and they follow the same trajectory, other than not hitting each other. After crossing each other, it takes 10 more minutes for missile A to reach its target. 90 minutes after the mid-air crossing, missile B reaches its target.
What is the ratio of the speed of missile A to missile B?
Let DA be the distance from missile A's launch point to the near-miss point
DB the distance from B's launch point to the near-miss point
VA and Vb the velocities of missiles A and B
It took the same time for missile A to travel distance DA as for B to travel DB:
DA / VA = DB / VB
It took 10 minutes for missile A to travel distance DB:
DB = VA x 10
It took 90 minutes for missile B to travel distance DA:
DA = VB x 90
DA / VA = (VB x 90) / VA
DB / VB = (VA x 10) / VB
Since DA / VA = DB / VB, (VB * 90) / VA = (VA x 10) / VB
VB2 x 90 = VA2 x 10
9 VB2 = VA2
(3 VB)2 = VA2
3 VB = VA
VA / VB = 3
Quote: beachbumbabsI'm having trouble with the idea that two missiles traveling same distance, same trajectory, could be at such different speeds to one another. 8:1? Not really a spoiler 'cuz it can't be right. One is a cannonball, the other a cruise missile, at least in my head.
I used different equations than ChesterDog, but wound up with the same type of equation to solve. Took me a few goes at the problem logic to get there.
