Will you please help solve this, with steps so I know how its done?

Question

After robbing a bank in Dodge City, a robber gallops off at 13 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?

Answer 1

Distance = Rate*Time ...  d=rt

 

Note that since the Marshall left 30 minutes later, his time riding

will be 30 minutes less than that of the robber:

 

Also note that since we are dealing with miles per hour, we need

to convert all our times to hours... 30 minutes = 0.5 hours

 

Robber:  d = 13(t)

Marshall: d = 16(t-.5)

 

We want to know the amount of time that passes until the distances are equal

 

16(t-.5) = 13t

16t - 8 = 13t

16t-13t = 8

3t = 8

t = 8/3 hours = 2 2/3 hours

 

2/3 hours = (2/3)(60 min/hr) = 40 minutes

 

The marshall will catch up with the robber in 2 hours 40 minutes