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

Kirk required 37.5 hours 
Marvin required 25 hours 

k = Kirk's speed
k+m = Marvin's speed
t = time it took them to meet in space.

In time t,
Kirk travelled kt
Marvin travelled (k+m)t

In time 22.5, Kirk travelled (k+m)t
In time 10, Marvin travelled kt

22.5 = (k+m)t/k
10 = kt/(k+m)

(k+m)t = 22.5k
kt = 10(k+m)

t = 22.5k/(k+m)
t = 10(k+m)/k

22.5k/(k+m) = 10(k+m)/k

22.5(k^2) = 10(k+m)(k+m)

(22.5/10)k^2 = (k+m)^2

1.5k = k+m

m = 0.5k 

Therefore Marvin's speed is 1.5 Kirks's speed

In time 22.5, Kirk travelled 1.5kt
In time 10, Marvin travelled kt

22.5 = 1.5kt/k
10 = kt/1.5k

t = 15 hours

Marvin took 15+10= 25 hours to complete his journey.

Kirk took 15+22.5 = 37.5 hours to complete his journey.

 

 

 

 

Edited on May 5, 2005, 10:31 am

Posted by Penny on 2005-05-05 10:28:09