SOLUTION: pt) 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 th

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: pt) 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 th      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 812408: pt) 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 by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What is the robber's head start?
+d%5B1%5D+=+13%2A%281%2F3%29+ ( converting 20 min to hrs )
+d%5B1%5D+=+13%2F3+
------------------
Start a stopwatch when the marshall leaves
Let +t+ = time on stopwatch when marshall
catches robber
Let +d+ = distance from Dodge City that
marshall catches robber
------------------
robber's equation:
(1) +d+-+13%2F3+=+13t+
marshall's equation:
(2) +d+=+16t+
--------------
(1) +3d+-+13+=+39t+
(1) +3d+=+39t+%2B+13+
---------------------
By substitution:
(1) +3%2A16t+=+39t+%2B+13+
(1) +48t+-+39t+=+13+
(1) +9t+=+13+
(1) +t+=+13%2F9+
(1) +t+=+1+%2B+4%2F9+ hrs
(1) +%284%2F9%29%2A60+=+27+ min
The marshall catches the robber in 1 hr and 27 min