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

Let their combined total times equal 1. The difference between 10 and 22.5 is 12.5, therefore the individual total times must be a multiple of 12.5, viz. 12.5, 25, 37.5, 50 ... of these, only 10/25 which is 0.4 and 22.5/37.5 which is 0.6 add to 1. Therefore, Kirk's time is 37.5 hours and Marvin's time is 25 hours.

Posted by CeeAnne on 2005-05-08 06:22:24