After robbing a bank in Dodge City, a robber gallops off at 13 mi/h. 20 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?

Answer 1

let the time taken by the robber when he is caught be t hrs
distance he covered = 13t miles

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

but 13t = 16(t - 1/3)
13t = 16t - 16/3
-3t = -16/3
t = 16/9 hrs

time of marshall = t - 1/3
= 16/9 - 1/3 = 13/9 hrs or 1 hour and appr 27 minutes