After robbing a bank in Dodge City,

Question

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

Answer 1

Hi Treena!

How far does robber go in 20 mins or 1/3 hour?    14/3 mile-gap when marshall starts.

Close the gap:  marshall has 2 mph edge over robber ... or 6/3 mph

after 1 hr - 2 miles, 2 hr -- 4 miles or 12/3 miles, 3 hr -- 6 miles or 18/3 miles ...

Answer: 2 hrs almost there -- need another 2/3 miles for the 14/3 mile-gap ...

for 6/3 mph edge, what part of the next hour covers 2/3 miles ...

looks like another 1/3 of an hour closes the gap -- 1/3 of 6/3mph = 2/3 miles

How about 2hrs 20mins?