When did C pass J? (Math Problem)?

H,C%26amp;J go east.


M goes west.


H meets C @ 11:22:33.


H meets J @ 13:05:10.


H meets M @ 14:57:08.


M met C@15:23:00.


M met J@15:47:42.


When did C pass J, assuming that they all take the same road and all have constant velocities?

When did C pass J? (Math Problem)?
Wicked! Who ever inflicted this thing on an unsuspecting world??





To begin with, convert all of your times to numbers of seconds, starting with HC at time 0:


HC at time 0 (Point 1)


HJ at time 6157 (Point 2)


HM at time 12875 (Point 3)


MC at time 14427 (Point 4)


MJ at time 15909 (Point 5)





Let us assume that H is walking east at 1 fps (foot per second).


Point 1 is at position 0


Point 2 is at position 6157


Point 3 is at position 12875





Let us assume that M is walking west at 1 fps. (M's speed can be any value provided M does not get back to point 2 (where H and J met) prior to meeting H, C and J first. Since everybody is moving at a constant speed, everything will adjust provided that the order of meetings happens as stated.)





Point 4 is at 12875-1552 = 11323


Point 5 is at 12875-3034 = 9841.





So then.





C travels from point 1 (starting at time 0 and point 0) to point 4, a distance of 11323, in 14427 seconds. C's speed is 11323/14427 fps.





J travels from point 2 (starting at time 6157 and point 6157) to point 5, a distance of 12875 - 6157 - 3034 = 3684, in 9752 seconds. J's speed is 3684/9752. Extrapolating back, we find that at time 0 (6157 seconds ago), she was at position 3684/9752 * 6157 = 9340169/2438





So then.





At time 0, you have C starting at point 0 and moving at 11323/14427 fps. You have J starting at point 9340169/2438 and moving at 3684/9752 fps. At time t, they will meet.





13323t/14427 = 9340169/2438 + 3684t/9752


13323t/14427 = 37360676/9752 + 3684t/9752


129925896t = 539002472652 + 53149068t


76776828t = 539002472652


t = 7020 17848/47025





So they meet at just over 7020 seconds after HC.





11:22:33 + 7020 seconds is 13:19:33.





I hope it helps, but frankly I'm somewhat beyond caring at this point. ;)