Afreight ship left port and was sailing due west at 24 knots. the steamship empress ann sailing due west at 32 knots left the same port 3 hours later. for how many hours had the steamship been traveling when the two ships had traveled exactly the same distance?

Let F be the distance traveled by the freight ship and E be the distance traveled by the steamship.
F = 24t 
E = 32(t - 3); t > 3 because the steamship departed with a 3 hour delay.
F and E will become equal when the ships have traveled the same distance.
24t = 32(t - 3)
24t = 32t - 96
8t = 96
t = 12 hours
After 12 hours, the ships will have traveled the exact same distance from the port.