Captain Kirk’s starship leaves Earth for Planet X at the same time Marvin the Martian’s starship leaves Planet X for Earth. Each ship travels at a constant velocity, but one is faster than the other. After meeting and passing, Kirk requires 22.5 hours to reach Planet X, while Marvin requires only 10 hours to reach Earth. Exactly what total time did each starship require for its interplanetary journey? Assume stationary planets.

Credit for this problem goes to Cliff Pickover

Say:

T = the time before the spaceships meet
Vk = Kirk's speed
Vm = Martin's speed
Dk = the distance travelled by Kirk before meeting
Dm = the distance already by Martin before meeting

Then, looking at both ships journey before and after the crossing:
Vk = Dk/T = Dm/22.5h   (Kirk's speed)
Vm = Dm/T = Dk/10h     (Martin's speed)

Which means:
Dk/Dm = T/22.5h = 10h/T

Which means:
T = 15h

Conclusion:
Kirk travels for 15h + 22.5h = 37.5h
Martin travels for 15h + 10h = 25h

And to add: scientists have discovered that space probes gradually loose speed whilst travelling through space. This shouldn't be the case if we are to believe the current laws of gravity...

Posted by Jurgen on 2005-05-05 13:02:38