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Call Kirk’s speed u, and Marvin’s speed v. Since they both left at the same moment, and then meet each other along the way, they both traveled the same amount of time over this portion of the journey. Call this amount of time t.
Therefore we have the following distances:
Dist. travelled by Kirk before meeting = tu
Dist. travelled by Marvin before meeting = tv
Dist. travelled by Kirk after meeting = 22.5 hours * u
Dist. travelled by Marvin after meeting = 10 hours * v
Notice:
Dist. travelled by Kirk before meeting = Dist. travelled by Marvin after meeting
So tu = (10hr)v
Dist. travelled by Marvin before meeting = Dist. travelled by Kirk after meeting
So tv = (22.5hr)u
tu = (10hr)v
t = (10hr)v/u
tv = (22.5hr)u
v = (22.5hr)u/t
t = (10hr)v/u = (10hr)*((22.5hr)u/t)/u = (225hr2)/t
t2 = 225hr2
t = 15 hours
So Kirk’s ship took 22.5+15 hours = 37.5 hours total.
And Marvin’s ship took 10+15 hours = 25 hours total.
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