After robbing a bank in Dodge City, a robber gallops off at 12 mi/h. 30 minutes later, the marshall leaves to pursue the robber at 16 mi/h.

How long (in hours) does it take the marshall to catch up to the robber?

1 answer

let the time taken by the robber when he is caught be t hrs
distance he covered = 12t miles

time taken by the marshall to catch him = t - 1/3
distance traveled by him = 16(t - 1/2)

but 12t = 16(t - 1/2)
12t = 16t - 16/2
-3t = -16/2
t = 8/3 hrs