After robbing a bank in Dodge City, a robber gallops off at 14 mi/h. 20 minutes later, the marshall leaves to pursue the robber at 16 mi/h?

Robber has run 20 minutes in advance. Therefore he hasheref already covered the distance
20/60*14=14/3 miles. The marshal starts half an hour later. He can cover a distance of (16-14) m in an hour, Therefore to cover the distance 14/3 miles he needs,
14/3*1/2 hours = 7/3 hours = 2 hours and twenty minutes.

Let t = time for marshall to catch the robber after the bank is robbed

Let VR = the robber's speed

Let VM = the marshall's speed

d = dR = ( VR ) ( t )

d = dM = ( VM ) ( t - 1/3 )

d = dR = dM = ( VR ) ( t ) = ( VM ) ( t - 1/3 )

( 14 ) ( t ) = ( 16 ) ( t - 1/3 ) = 16t - 16/3

Multiply both sides by 3 and get :

( 48 ) ( t ) = ( 48 ) ( t ) - 16

6t = 16

t = 16/6 = 8/3 h = 2 2/3 h <-------------------

Check the answer :
-------------------------------

dR = ( 14 mi/h ) ( 8/3 h ) = 112/3 mi = 37 1/3 mi<----------------

dM = ( 16 mi/h ) ( ( 8/3 - 1/3 ) = ( 16 mi/h ) ( 7/3 h ) = 112/3 mi = 37 1/3 mi <----

d = dR = dM = 37 1/3 mi -----------> [ OK ]